/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 301 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (14) CpxTRS (15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (16) CpxRelTRS (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 1 ms] (22) CpxTypedWeightedCompleteTrs (23) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 30 ms] (24) CpxRNTS (25) CompletionProof [UPPER BOUND(ID), 6 ms] (26) CpxTypedWeightedCompleteTrs (27) NarrowingProof [BOTH BOUNDS(ID, ID), 182 ms] (28) CpxTypedWeightedCompleteTrs (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms] (30) CpxRNTS (31) SimplificationProof [BOTH BOUNDS(ID, 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), 53 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 73 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 110 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 282 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 121 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app'(app'(minus, x), 0) -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0), app'(s, y)) -> 0 app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(minus, x), 0) -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0), app'(s, y)) -> 0 app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(minus, x), 0) -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0), app'(s, y)) -> 0 app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(minus, x), 0) -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0), app'(s, y)) -> 0 app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(minus, x), 0') -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0'), app'(s, y)) -> 0' app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0'), y) -> true app'(app'(le, app'(s, x)), 0') -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, 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(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0' encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(minus, x), 0') -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0'), app'(s, y)) -> 0' app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0'), y) -> true app'(app'(le, app'(s, x)), 0') -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) app'(app'(app'(app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) encArg(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0' encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 Types: app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' minus :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' 0' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' s :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' quot :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' le :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' true :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' false :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' app :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' nil :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' add :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' if_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' if_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' quicksort :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' map :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' filter :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' filter2 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encArg :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' cons_app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_minus :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_0 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_s :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_quot :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_le :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_true :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_false :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_app :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_nil :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_add :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_if_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_if_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_quicksort :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_map :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_filter :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_filter2 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' hole_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'1_3 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' gen_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'2_3 :: Nat -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort: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'(minus, x), 0') -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0'), app'(s, y)) -> 0' app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0'), y) -> true app'(app'(le, app'(s, x)), 0') -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) app'(app'(app'(app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) encArg(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0' encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 Types: app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' minus :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' 0' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' s :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' quot :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' le :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' true :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' false :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' app :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' nil :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' add :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' if_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' if_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' quicksort :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' map :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' filter :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' filter2 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encArg :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' cons_app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_app' :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_minus :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_0 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_s :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_quot :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_le :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_true :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_false :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_app :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_nil :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_add :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_if_low :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_if_high :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_quicksort :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_map :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_filter :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' encode_filter2 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' hole_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'1_3 :: minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' gen_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'2_3 :: Nat -> minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app' Generator Equations: gen_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'2_3(0) <=> minus gen_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'2_3(+(x, 1)) <=> cons_app'(minus, gen_minus:0':s:quot:le:true:false:app:nil:add:low:if_low:high:if_high:quicksort:map:filter:filter2:cons_app'2_3(x)) The following defined symbols remain to be analysed: app', encArg They will be analysed ascendingly in the following order: app' < encArg ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app'(app'(minus, x), 0) -> x app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y) app'(app'(quot, 0), app'(s, y)) -> 0 app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(app'(low, n), nil) -> nil app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x) app'(app'(high, n), nil) -> nil app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x) app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(app'(map, f), nil) -> nil app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) app'(app'(filter, f), nil) -> nil app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) app'(app'(app'(app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(quicksort, nil) -> nil app'(c_app'(quot, 0), c_app'(s, y)) -> 0 app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) app'(c_app'(le, c_app'(s, x)), 0) -> false app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(high, n), x) app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) app'(c_app'(low, n), nil) -> nil app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(c_app'(high, n), nil) -> nil app'(c_app'(le, c_app'(s, x)), c_app'(s, y)) -> app'(app'(le, x), y) app'(c_app'(app, nil), y) -> y app'(c_app'(map, f), nil) -> nil app'(c_app'(minus, x), 0) -> x app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(app'(minus, x), y) app'(c_app'(le, 0), y) -> true app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) app'(c_app'(filter, f), nil) -> nil app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(low, n), x) app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort 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'(quicksort, nil) -> nil [1] app'(c_app'(quot, 0), c_app'(s, y)) -> 0 [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) [1] app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) [1] app'(c_app'(le, c_app'(s, x)), 0) -> false [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(high, n), x) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) [1] app'(c_app'(low, n), nil) -> nil [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) [1] app'(c_app'(high, n), nil) -> nil [1] app'(c_app'(le, c_app'(s, x)), c_app'(s, y)) -> app'(app'(le, x), y) [1] app'(c_app'(app, nil), y) -> y [1] app'(c_app'(map, f), nil) -> nil [1] app'(c_app'(minus, x), 0) -> x [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(app'(minus, x), y) [1] app'(c_app'(le, 0), y) -> true [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(filter, f), nil) -> nil [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(low, n), x) [1] app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(quot) -> quot [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(app) -> app [0] encArg(nil) -> nil [0] encArg(add) -> add [0] encArg(low) -> low [0] encArg(if_low) -> if_low [0] encArg(high) -> high [0] encArg(if_high) -> if_high [0] encArg(quicksort) -> quicksort [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_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_quot -> quot [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_app -> app [0] encode_nil -> nil [0] encode_add -> add [0] encode_low -> low [0] encode_if_low -> if_low [0] encode_high -> high [0] encode_if_high -> if_high [0] encode_quicksort -> quicksort [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'(quicksort, nil) -> nil [1] app'(c_app'(quot, 0), c_app'(s, y)) -> 0 [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) [1] app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) [1] app'(c_app'(le, c_app'(s, x)), 0) -> false [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(high, n), x) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) [1] app'(c_app'(low, n), nil) -> nil [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) [1] app'(c_app'(high, n), nil) -> nil [1] app'(c_app'(le, c_app'(s, x)), c_app'(s, y)) -> app'(app'(le, x), y) [1] app'(c_app'(app, nil), y) -> y [1] app'(c_app'(map, f), nil) -> nil [1] app'(c_app'(minus, x), 0) -> x [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(app'(minus, x), y) [1] app'(c_app'(le, 0), y) -> true [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(filter, f), nil) -> nil [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(low, n), x) [1] app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(quot) -> quot [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(app) -> app [0] encArg(nil) -> nil [0] encArg(add) -> add [0] encArg(low) -> low [0] encArg(if_low) -> if_low [0] encArg(high) -> high [0] encArg(if_high) -> if_high [0] encArg(quicksort) -> quicksort [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_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_quot -> quot [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_app -> app [0] encode_nil -> nil [0] encode_add -> add [0] encode_low -> low [0] encode_if_low -> if_low [0] encode_high -> high [0] encode_if_high -> if_high [0] encode_quicksort -> quicksort [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' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' c_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' 0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' cons_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app' Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_app'(v0, v1) -> null_encode_app' [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_quot -> null_encode_quot [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_app -> null_encode_app [0] encode_nil -> null_encode_nil [0] encode_add -> null_encode_add [0] encode_low -> null_encode_low [0] encode_if_low -> null_encode_if_low [0] encode_high -> null_encode_high [0] encode_if_high -> null_encode_if_high [0] encode_quicksort -> null_encode_quicksort [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_minus, null_encode_0, null_encode_s, null_encode_quot, null_encode_le, null_encode_true, null_encode_false, null_encode_app, null_encode_nil, null_encode_add, null_encode_low, null_encode_if_low, null_encode_high, null_encode_if_high, null_encode_quicksort, null_encode_map, null_encode_filter, null_encode_filter2, null_app' ---------------------------------------- (22) 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'(quicksort, nil) -> nil [1] app'(c_app'(quot, 0), c_app'(s, y)) -> 0 [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) [1] app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) [1] app'(c_app'(le, c_app'(s, x)), 0) -> false [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(high, n), x) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) [1] app'(c_app'(low, n), nil) -> nil [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) [1] app'(c_app'(high, n), nil) -> nil [1] app'(c_app'(le, c_app'(s, x)), c_app'(s, y)) -> app'(app'(le, x), y) [1] app'(c_app'(app, nil), y) -> y [1] app'(c_app'(map, f), nil) -> nil [1] app'(c_app'(minus, x), 0) -> x [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(app'(minus, x), y) [1] app'(c_app'(le, 0), y) -> true [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(filter, f), nil) -> nil [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(low, n), x) [1] app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(quot) -> quot [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(app) -> app [0] encArg(nil) -> nil [0] encArg(add) -> add [0] encArg(low) -> low [0] encArg(if_low) -> if_low [0] encArg(high) -> high [0] encArg(if_high) -> if_high [0] encArg(quicksort) -> quicksort [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_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_quot -> quot [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_app -> app [0] encode_nil -> nil [0] encode_add -> add [0] encode_low -> low [0] encode_if_low -> if_low [0] encode_high -> high [0] encode_if_high -> if_high [0] encode_quicksort -> quicksort [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_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_quot -> null_encode_quot [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_app -> null_encode_app [0] encode_nil -> null_encode_nil [0] encode_add -> null_encode_add [0] encode_low -> null_encode_low [0] encode_if_low -> null_encode_if_low [0] encode_high -> null_encode_high [0] encode_if_high -> null_encode_if_high [0] encode_quicksort -> null_encode_quicksort [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' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' c_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' 0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' cons_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' Rewrite Strategy: INNERMOST ---------------------------------------- (23) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: quicksort => 14 nil => 13 quot => 15 0 => 0 s => 16 add => 1 app => 2 low => 10 high => 6 if_high => 7 false => 3 filter => 4 filter2 => 5 le => 9 true => 17 minus => 12 if_low => 8 map => 11 null_encArg => 0 null_encode_app' => 0 null_encode_minus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_quot => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_app => 0 null_encode_nil => 0 null_encode_add => 0 null_encode_low => 0 null_encode_if_low => 0 null_encode_high => 0 null_encode_if_high => 0 null_encode_quicksort => 0 null_encode_map => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_app' => 0 ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: app'(z, z') -{ 1 }-> x :|: z = 1 + 12 + x, x >= 0, z' = 0 app'(z, z') -{ 1 }-> y :|: y >= 0, z = 1 + 2 + 13, z' = y app'(z, z') -{ 1 }-> app'(app'(app'(app'(5, app'(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(app'(9, m), n)), n), app'(app'(1, m), x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 10 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(app'(9, m), n)), n), app'(app'(1, m), x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 6 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(9, x), y) :|: z' = 1 + 16 + y, z = 1 + 9 + (1 + 16 + x), x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(app'(6, n), x) :|: z = 1 + (1 + 7 + 17) + n, n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(4, f), xs) :|: f >= 0, xs >= 0, z = 1 + (1 + (1 + 5 + 3) + f) + x, x >= 0, z' = xs app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(app'(10, n), x))), app'(app'(1, n), app'(14, app'(app'(6, n), x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(12, x), y) :|: z' = 1 + 16 + y, x >= 0, y >= 0, z = 1 + 12 + (1 + 16 + x) app'(z, z') -{ 1 }-> app'(app'(10, n), x) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 3) + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(1, m), app'(app'(6, n), x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, z = 1 + (1 + 7 + 3) + n, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(1, m), app'(app'(10, n), x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 17) + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(1, n), app'(app'(2, x), y)) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, y >= 0, z' = y app'(z, z') -{ 1 }-> app'(app'(1, x), app'(app'(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(app'(1, app'(f, x)), app'(app'(11, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 11 + f, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(app'(12, x), y)), app'(16, y))) :|: z = 1 + 15 + (1 + 16 + x), z' = 1 + 16 + y, x >= 0, y >= 0 app'(z, z') -{ 1 }-> 3 :|: z = 1 + 9 + (1 + 16 + x), x >= 0, z' = 0 app'(z, z') -{ 1 }-> 17 :|: z = 1 + 9 + 0, y >= 0, z' = y app'(z, z') -{ 1 }-> 13 :|: z = 14, z' = 13 app'(z, z') -{ 1 }-> 13 :|: n >= 0, z = 1 + 10 + n, z' = 13 app'(z, z') -{ 1 }-> 13 :|: n >= 0, z = 1 + 6 + n, z' = 13 app'(z, z') -{ 1 }-> 13 :|: f >= 0, z = 1 + 11 + f, z' = 13 app'(z, z') -{ 1 }-> 13 :|: f >= 0, z = 1 + 4 + f, z' = 13 app'(z, z') -{ 1 }-> 0 :|: z' = 1 + 16 + y, y >= 0, z = 1 + 15 + 0 app'(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app'(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app'(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 9 :|: z = 9 encArg(z) -{ 0 }-> 8 :|: z = 8 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 17 :|: z = 17 encArg(z) -{ 0 }-> 16 :|: z = 16 encArg(z) -{ 0 }-> 15 :|: z = 15 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_add -{ 0 }-> 1 :|: encode_add -{ 0 }-> 0 :|: encode_app -{ 0 }-> 2 :|: encode_app -{ 0 }-> 0 :|: encode_app'(z, z') -{ 0 }-> app'(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app'(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_high -{ 0 }-> 6 :|: encode_high -{ 0 }-> 0 :|: encode_if_high -{ 0 }-> 7 :|: encode_if_high -{ 0 }-> 0 :|: encode_if_low -{ 0 }-> 8 :|: encode_if_low -{ 0 }-> 0 :|: encode_le -{ 0 }-> 9 :|: encode_le -{ 0 }-> 0 :|: encode_low -{ 0 }-> 10 :|: encode_low -{ 0 }-> 0 :|: encode_map -{ 0 }-> 11 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 12 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 13 :|: encode_nil -{ 0 }-> 0 :|: encode_quicksort -{ 0 }-> 14 :|: encode_quicksort -{ 0 }-> 0 :|: encode_quot -{ 0 }-> 15 :|: encode_quot -{ 0 }-> 0 :|: encode_s -{ 0 }-> 16 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 17 :|: encode_true -{ 0 }-> 0 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (25) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_app'_2 encode_minus encode_0 encode_s encode_quot encode_le encode_true encode_false encode_app encode_nil encode_add encode_low encode_if_low encode_high encode_if_high encode_quicksort 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_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_quot -> null_encode_quot [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_app -> null_encode_app [0] encode_nil -> null_encode_nil [0] encode_add -> null_encode_add [0] encode_low -> null_encode_low [0] encode_if_low -> null_encode_if_low [0] encode_high -> null_encode_high [0] encode_if_high -> null_encode_if_high [0] encode_quicksort -> null_encode_quicksort [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_minus, null_encode_0, null_encode_s, null_encode_quot, null_encode_le, null_encode_true, null_encode_false, null_encode_app, null_encode_nil, null_encode_add, null_encode_low, null_encode_if_low, null_encode_high, null_encode_if_high, null_encode_quicksort, null_encode_map, null_encode_filter, null_encode_filter2, null_app' ---------------------------------------- (26) 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'(quicksort, nil) -> nil [1] app'(c_app'(quot, 0), c_app'(s, y)) -> 0 [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x)))) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x)) [1] app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) [1] app'(c_app'(le, c_app'(s, x)), 0) -> false [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(high, n), x) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y))) [1] app'(c_app'(low, n), nil) -> nil [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) [1] app'(c_app'(high, n), nil) -> nil [1] app'(c_app'(le, c_app'(s, x)), c_app'(s, y)) -> app'(app'(le, x), y) [1] app'(c_app'(app, nil), y) -> y [1] app'(c_app'(map, f), nil) -> nil [1] app'(c_app'(minus, x), 0) -> x [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(app'(minus, x), y) [1] app'(c_app'(le, 0), y) -> true [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x)) [1] app'(c_app'(filter, f), nil) -> nil [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(app'(low, n), x) [1] app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(quot) -> quot [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(app) -> app [0] encArg(nil) -> nil [0] encArg(add) -> add [0] encArg(low) -> low [0] encArg(if_low) -> if_low [0] encArg(high) -> high [0] encArg(if_high) -> if_high [0] encArg(quicksort) -> quicksort [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_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_quot -> quot [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_app -> app [0] encode_nil -> nil [0] encode_add -> add [0] encode_low -> low [0] encode_if_low -> if_low [0] encode_high -> high [0] encode_if_high -> if_high [0] encode_quicksort -> quicksort [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_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_quot -> null_encode_quot [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_app -> null_encode_app [0] encode_nil -> null_encode_nil [0] encode_add -> null_encode_add [0] encode_low -> null_encode_low [0] encode_if_low -> null_encode_if_low [0] encode_high -> null_encode_high [0] encode_if_high -> null_encode_if_high [0] encode_quicksort -> null_encode_quicksort [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' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' c_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' 0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' cons_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' Rewrite Strategy: INNERMOST ---------------------------------------- (27) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (28) 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'(quicksort, nil) -> nil [1] app'(c_app'(quot, 0), c_app'(s, y)) -> 0 [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(c_app'(low, n), x))), app'(c_app'(add, n), app'(quicksort, app'(c_app'(high, n), x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(c_app'(low, n), x))), app'(c_app'(add, n), app'(quicksort, app'(null_app', x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(c_app'(low, n), x))), app'(null_app', app'(quicksort, app'(c_app'(high, n), x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(c_app'(low, n), x))), app'(null_app', app'(quicksort, app'(null_app', x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(null_app', x))), app'(c_app'(add, n), app'(quicksort, app'(c_app'(high, n), x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(null_app', x))), app'(c_app'(add, n), app'(quicksort, app'(null_app', x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(null_app', x))), app'(null_app', app'(quicksort, app'(c_app'(high, n), x)))) [1] app'(quicksort, c_app'(c_app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(null_app', x))), app'(null_app', app'(quicksort, app'(null_app', x)))) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(add, m), app'(c_app'(high, n), x)) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(add, m), app'(null_app', x)) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(null_app', app'(c_app'(high, n), x)) [1] app'(c_app'(c_app'(if_high, false), n), c_app'(c_app'(add, m), x)) -> app'(null_app', app'(null_app', x)) [1] app'(c_app'(filter, f), c_app'(c_app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs) [1] app'(c_app'(le, c_app'(s, x)), 0) -> false [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(high, n), x) [1] app'(c_app'(c_app'(if_high, true), n), c_app'(c_app'(add, m), x)) -> app'(null_app', x) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(c_app'(minus, x), y)), c_app'(s, y))) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(c_app'(minus, x), y)), null_app')) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(null_app', y)), c_app'(s, y))) [1] app'(c_app'(quot, c_app'(s, x)), c_app'(s, y)) -> app'(s, app'(app'(quot, app'(null_app', y)), null_app')) [1] app'(c_app'(low, n), nil) -> nil [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(c_app'(le, m), n)), n), app'(c_app'(add, m), x)) [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(c_app'(le, m), n)), n), app'(null_app', x)) [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(null_app', n)), n), app'(c_app'(add, m), x)) [1] app'(c_app'(low, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_low, app'(null_app', n)), n), app'(null_app', x)) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(c_app'(filter, f), xs) [1] app'(c_app'(c_app'(c_app'(filter2, false), f), x), xs) -> app'(null_app', xs) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(c_app'(add, x), app'(c_app'(filter, f), xs)) [1] app'(c_app'(c_app'(c_app'(filter2, true), f), x), xs) -> app'(c_app'(add, 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'(app, c_app'(c_app'(add, n), x)), y) -> app'(c_app'(add, n), app'(c_app'(app, x), y)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(c_app'(add, n), app'(null_app', y)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(null_app', app'(c_app'(app, x), y)) [1] app'(c_app'(app, c_app'(c_app'(add, n), x)), y) -> app'(null_app', app'(null_app', y)) [1] app'(c_app'(high, n), nil) -> nil [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'(app, nil), y) -> y [1] app'(c_app'(map, f), nil) -> nil [1] app'(c_app'(minus, x), 0) -> x [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(c_app'(minus, x), y) [1] app'(c_app'(minus, c_app'(s, x)), c_app'(s, y)) -> app'(null_app', y) [1] app'(c_app'(le, 0), y) -> true [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(add, m), app'(c_app'(low, n), x)) [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(add, m), app'(null_app', x)) [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(null_app', app'(c_app'(low, n), x)) [1] app'(c_app'(c_app'(if_low, true), n), c_app'(c_app'(add, m), x)) -> app'(null_app', app'(null_app', x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(c_app'(le, m), n)), n), app'(c_app'(add, m), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(c_app'(le, m), n)), n), app'(null_app', x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(null_app', n)), n), app'(c_app'(add, m), x)) [1] app'(c_app'(high, n), c_app'(c_app'(add, m), x)) -> app'(app'(app'(if_high, app'(null_app', n)), n), app'(null_app', x)) [1] app'(c_app'(filter, f), nil) -> nil [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(c_app'(low, n), x) [1] app'(c_app'(c_app'(if_low, false), n), c_app'(c_app'(add, m), x)) -> app'(null_app', x) [1] app'(c_app'(map, f), c_app'(c_app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs)) [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(quot) -> quot [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(app) -> app [0] encArg(nil) -> nil [0] encArg(add) -> add [0] encArg(low) -> low [0] encArg(if_low) -> if_low [0] encArg(high) -> high [0] encArg(if_high) -> if_high [0] encArg(quicksort) -> quicksort [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_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_quot -> quot [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_app -> app [0] encode_nil -> nil [0] encode_add -> add [0] encode_low -> low [0] encode_if_low -> if_low [0] encode_high -> high [0] encode_if_high -> if_high [0] encode_quicksort -> quicksort [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_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_quot -> null_encode_quot [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_app -> null_encode_app [0] encode_nil -> null_encode_nil [0] encode_add -> null_encode_add [0] encode_low -> null_encode_low [0] encode_if_low -> null_encode_if_low [0] encode_high -> null_encode_high [0] encode_if_high -> null_encode_if_high [0] encode_quicksort -> null_encode_quicksort [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' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' c_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' 0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' cons_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' -> quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encArg :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_minus :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_0 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_s :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quot :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_le :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_true :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_false :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_app :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_nil :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_add :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_low :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_if_high :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_quicksort :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_map :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_encode_filter2 :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' null_app' :: quicksort:nil:quot:0:c_app':s:add:app:low:high:if_high:false:filter:filter2:le:true:minus:if_low:map:cons_app':null_encArg:null_encode_app':null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_le:null_encode_true:null_encode_false:null_encode_app:null_encode_nil:null_encode_add:null_encode_low:null_encode_if_low:null_encode_high:null_encode_if_high:null_encode_quicksort:null_encode_map:null_encode_filter:null_encode_filter2:null_app' Rewrite Strategy: INNERMOST ---------------------------------------- (29) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: quicksort => 14 nil => 13 quot => 15 0 => 0 s => 16 add => 1 app => 2 low => 10 high => 6 if_high => 7 false => 3 filter => 4 filter2 => 5 le => 9 true => 17 minus => 12 if_low => 8 map => 11 null_encArg => 0 null_encode_app' => 0 null_encode_minus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_quot => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_app => 0 null_encode_nil => 0 null_encode_add => 0 null_encode_low => 0 null_encode_if_low => 0 null_encode_high => 0 null_encode_if_high => 0 null_encode_quicksort => 0 null_encode_map => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_app' => 0 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: app'(z, z') -{ 1 }-> x :|: z = 1 + 12 + x, x >= 0, z' = 0 app'(z, z') -{ 1 }-> y :|: y >= 0, z = 1 + 2 + 13, z' = y app'(z, z') -{ 1 }-> app'(app'(app'(app'(5, app'(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(0, n)), n), app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 10 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(0, n)), n), app'(1 + 1 + m, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 10 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(1 + 9 + m, n)), n), app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 10 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(1 + 9 + m, n)), n), app'(1 + 1 + m, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 10 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(0, n)), n), app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 6 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(0, n)), n), app'(1 + 1 + m, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 6 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(1 + 9 + m, n)), n), app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 6 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(1 + 9 + m, n)), n), app'(1 + 1 + m, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + 6 + n, m >= 0 app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(0, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(0, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(1 + 1 + n, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(1 + 1 + n, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(0, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(0, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(1 + 1 + n, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(1 + 1 + n, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(1, app'(f, x)), app'(app'(11, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 11 + f, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(0, y)), 0)) :|: z = 1 + 15 + (1 + 16 + x), z' = 1 + 16 + y, x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(0, y)), 1 + 16 + y)) :|: z = 1 + 15 + (1 + 16 + x), z' = 1 + 16 + y, x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(1 + 12 + x, y)), 0)) :|: z = 1 + 15 + (1 + 16 + x), z' = 1 + 16 + y, x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(1 + 12 + x, y)), 1 + 16 + y)) :|: z = 1 + 15 + (1 + 16 + x), z' = 1 + 16 + y, x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(0, x) :|: z = 1 + (1 + 7 + 17) + n, n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, x) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 3) + n, m >= 0 app'(z, z') -{ 1 }-> app'(0, xs) :|: f >= 0, xs >= 0, z = 1 + (1 + (1 + 5 + 3) + f) + x, x >= 0, z' = xs app'(z, z') -{ 1 }-> app'(0, y) :|: z' = 1 + 16 + y, z = 1 + 9 + (1 + 16 + x), x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(0, y) :|: z' = 1 + 16 + y, x >= 0, y >= 0, z = 1 + 12 + (1 + 16 + x) app'(z, z') -{ 1 }-> app'(0, app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, z = 1 + (1 + 7 + 3) + n, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 17) + n, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(0, app'(0, y)) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, y >= 0, z' = y app'(z, z') -{ 1 }-> app'(0, app'(1 + 6 + n, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, z = 1 + (1 + 7 + 3) + n, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(1 + 4 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(0, app'(1 + 2 + x, y)) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, y >= 0, z' = y app'(z, z') -{ 1 }-> app'(0, app'(1 + 10 + n, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 17) + n, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 9 + x, y) :|: z' = 1 + 16 + y, z = 1 + 9 + (1 + 16 + x), x >= 0, y >= 0 app'(z, z') -{ 1 }-> app'(1 + 6 + n, x) :|: z = 1 + (1 + 7 + 17) + n, n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 4 + f, xs) :|: f >= 0, xs >= 0, z = 1 + (1 + (1 + 5 + 3) + f) + x, x >= 0, z' = xs app'(z, z') -{ 1 }-> app'(1 + 12 + x, y) :|: z' = 1 + 16 + y, x >= 0, y >= 0, z = 1 + 12 + (1 + 16 + x) app'(z, z') -{ 1 }-> app'(1 + 10 + n, x) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 3) + n, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, z = 1 + (1 + 7 + 3) + n, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(0, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 17) + n, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(1 + 6 + n, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, z = 1 + (1 + 7 + 3) + n, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(1 + 10 + n, x)) :|: n >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, z = 1 + (1 + 8 + 17) + n, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + n, app'(0, y)) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, y >= 0, z' = y app'(z, z') -{ 1 }-> app'(1 + 1 + n, app'(1 + 2 + x, y)) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, y >= 0, z' = y app'(z, z') -{ 1 }-> app'(1 + 1 + x, app'(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(1 + 1 + x, app'(1 + 4 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> 3 :|: z = 1 + 9 + (1 + 16 + x), x >= 0, z' = 0 app'(z, z') -{ 1 }-> 17 :|: z = 1 + 9 + 0, y >= 0, z' = y app'(z, z') -{ 1 }-> 13 :|: z = 14, z' = 13 app'(z, z') -{ 1 }-> 13 :|: n >= 0, z = 1 + 10 + n, z' = 13 app'(z, z') -{ 1 }-> 13 :|: n >= 0, z = 1 + 6 + n, z' = 13 app'(z, z') -{ 1 }-> 13 :|: f >= 0, z = 1 + 11 + f, z' = 13 app'(z, z') -{ 1 }-> 13 :|: f >= 0, z = 1 + 4 + f, z' = 13 app'(z, z') -{ 1 }-> 0 :|: z' = 1 + 16 + y, y >= 0, z = 1 + 15 + 0 app'(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app'(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app'(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 9 :|: z = 9 encArg(z) -{ 0 }-> 8 :|: z = 8 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 17 :|: z = 17 encArg(z) -{ 0 }-> 16 :|: z = 16 encArg(z) -{ 0 }-> 15 :|: z = 15 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_add -{ 0 }-> 1 :|: encode_add -{ 0 }-> 0 :|: encode_app -{ 0 }-> 2 :|: encode_app -{ 0 }-> 0 :|: encode_app'(z, z') -{ 0 }-> app'(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app'(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_high -{ 0 }-> 6 :|: encode_high -{ 0 }-> 0 :|: encode_if_high -{ 0 }-> 7 :|: encode_if_high -{ 0 }-> 0 :|: encode_if_low -{ 0 }-> 8 :|: encode_if_low -{ 0 }-> 0 :|: encode_le -{ 0 }-> 9 :|: encode_le -{ 0 }-> 0 :|: encode_low -{ 0 }-> 10 :|: encode_low -{ 0 }-> 0 :|: encode_map -{ 0 }-> 11 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 12 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 13 :|: encode_nil -{ 0 }-> 0 :|: encode_quicksort -{ 0 }-> 14 :|: encode_quicksort -{ 0 }-> 0 :|: encode_quot -{ 0 }-> 15 :|: encode_quot -{ 0 }-> 0 :|: encode_s -{ 0 }-> 16 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 17 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (31) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: app'(z, z') -{ 1 }-> z' :|: z' >= 0, z = 1 + 2 + 13 app'(z, z') -{ 1 }-> app'(app'(app'(app'(5, app'(z - 5, x)), z - 5), x), xs) :|: z - 5 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(0, z - 11)), z - 11), app'(0, x)) :|: z - 11 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(0, z - 11)), z - 11), app'(1 + 1 + m, x)) :|: z - 11 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(1 + 9 + m, z - 11)), z - 11), app'(0, x)) :|: z - 11 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(8, app'(1 + 9 + m, z - 11)), z - 11), app'(1 + 1 + m, x)) :|: z - 11 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(0, z - 7)), z - 7), app'(0, x)) :|: z - 7 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(0, z - 7)), z - 7), app'(1 + 1 + m, x)) :|: z - 7 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(1 + 9 + m, z - 7)), z - 7), app'(0, x)) :|: z - 7 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(app'(7, app'(1 + 9 + m, z - 7)), z - 7), app'(1 + 1 + m, x)) :|: z - 7 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(0, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(0, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(1 + 1 + n, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(0, x))), app'(1 + 1 + n, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(0, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(0, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(1 + 1 + n, app'(14, app'(0, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(2, app'(14, app'(1 + 10 + n, x))), app'(1 + 1 + n, app'(14, app'(1 + 6 + n, x)))) :|: n >= 0, x >= 0, z = 14, z' = 1 + (1 + 1 + n) + x app'(z, z') -{ 1 }-> app'(app'(1, app'(z - 12, x)), app'(app'(11, z - 12), xs)) :|: z - 12 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(0, z' - 17)), 0)) :|: z - 33 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(0, z' - 17)), 1 + 16 + (z' - 17))) :|: z - 33 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(1 + 12 + (z - 33), z' - 17)), 0)) :|: z - 33 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(16, app'(app'(15, app'(1 + 12 + (z - 33), z' - 17)), 1 + 16 + (z' - 17))) :|: z - 33 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(0, x) :|: z - 26 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, x) :|: z - 13 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, z') :|: f >= 0, z' >= 0, z = 1 + (1 + (1 + 5 + 3) + f) + x, x >= 0 app'(z, z') -{ 1 }-> app'(0, app'(0, x)) :|: z - 12 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(0, x)) :|: z - 27 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(0, app'(0, z')) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, z' >= 0 app'(z, z') -{ 1 }-> app'(0, app'(1 + 6 + (z - 12), x)) :|: z - 12 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, app'(1 + 4 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(0, app'(1 + 2 + x, z')) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, z' >= 0 app'(z, z') -{ 1 }-> app'(0, app'(1 + 10 + (z - 27), x)) :|: z - 27 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(0, z' - 17) :|: z - 27 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(0, z' - 17) :|: z - 30 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(1 + 9 + (z - 27), z' - 17) :|: z - 27 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(1 + 6 + (z - 26), x) :|: z - 26 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 4 + f, z') :|: f >= 0, z' >= 0, z = 1 + (1 + (1 + 5 + 3) + f) + x, x >= 0 app'(z, z') -{ 1 }-> app'(1 + 12 + (z - 30), z' - 17) :|: z - 30 >= 0, z' - 17 >= 0 app'(z, z') -{ 1 }-> app'(1 + 10 + (z - 13), x) :|: z - 13 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(0, x)) :|: z - 12 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(0, x)) :|: z - 27 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(1 + 6 + (z - 12), x)) :|: z - 12 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + m, app'(1 + 10 + (z - 27), x)) :|: z - 27 >= 0, z' = 1 + (1 + 1 + m) + x, x >= 0, m >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + n, app'(0, z')) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, z' >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + n, app'(1 + 2 + x, z')) :|: n >= 0, z = 1 + 2 + (1 + (1 + 1 + n) + x), x >= 0, z' >= 0 app'(z, z') -{ 1 }-> app'(1 + 1 + x, app'(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> app'(1 + 1 + x, app'(1 + 4 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 5 + 17) + f) + x app'(z, z') -{ 1 }-> 3 :|: z - 27 >= 0, z' = 0 app'(z, z') -{ 1 }-> 17 :|: z = 1 + 9 + 0, z' >= 0 app'(z, z') -{ 1 }-> 13 :|: z = 14, z' = 13 app'(z, z') -{ 1 }-> 13 :|: z - 11 >= 0, z' = 13 app'(z, z') -{ 1 }-> 13 :|: z - 7 >= 0, z' = 13 app'(z, z') -{ 1 }-> 13 :|: z - 12 >= 0, z' = 13 app'(z, z') -{ 1 }-> 13 :|: z - 5 >= 0, z' = 13 app'(z, z') -{ 1 }-> 0 :|: z' - 17 >= 0, z = 1 + 15 + 0 app'(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 app'(z, z') -{ 1 }-> z - 13 :|: z - 13 >= 0, z' = 0 app'(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> app'(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 9 :|: z = 9 encArg(z) -{ 0 }-> 8 :|: z = 8 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 17 :|: z = 17 encArg(z) -{ 0 }-> 16 :|: z = 16 encArg(z) -{ 0 }-> 15 :|: z = 15 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_add -{ 0 }-> 1 :|: encode_add -{ 0 }-> 0 :|: encode_app -{ 0 }-> 2 :|: encode_app -{ 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_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_high -{ 0 }-> 6 :|: encode_high -{ 0 }-> 0 :|: encode_if_high -{ 0 }-> 7 :|: encode_if_high -{ 0 }-> 0 :|: encode_if_low -{ 0 }-> 8 :|: encode_if_low -{ 0 }-> 0 :|: encode_le -{ 0 }-> 9 :|: encode_le -{ 0 }-> 0 :|: encode_low -{ 0 }-> 10 :|: encode_low -{ 0 }-> 0 :|: encode_map -{ 0 }-> 11 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 12 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 13 :|: encode_nil -{ 0 }-> 0 :|: encode_quicksort -{ 0 }-> 14 :|: encode_quicksort -{ 0 }-> 0 :|: encode_quot -{ 0 }-> 15 :|: encode_quot -{ 0 }-> 0 :|: encode_s -{ 0 }-> 16 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 17 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (33) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: ENCARG(minus) -> c ENCARG(0) -> c1 ENCARG(s) -> c2 ENCARG(quot) -> c3 ENCARG(le) -> c4 ENCARG(true) -> c5 ENCARG(false) -> c6 ENCARG(app) -> c7 ENCARG(nil) -> c8 ENCARG(add) -> c9 ENCARG(low) -> c10 ENCARG(if_low) -> c11 ENCARG(high) -> c12 ENCARG(if_high) -> c13 ENCARG(quicksort) -> c14 ENCARG(map) -> c15 ENCARG(filter) -> c16 ENCARG(filter2) -> c17 ENCARG(cons_app'(z0, z1)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP'(z0, z1) -> c19(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MINUS -> c20 ENCODE_0 -> c21 ENCODE_S -> c22 ENCODE_QUOT -> c23 ENCODE_LE -> c24 ENCODE_TRUE -> c25 ENCODE_FALSE -> c26 ENCODE_APP -> c27 ENCODE_NIL -> c28 ENCODE_ADD -> c29 ENCODE_LOW -> c30 ENCODE_IF_LOW -> c31 ENCODE_HIGH -> c32 ENCODE_IF_HIGH -> c33 ENCODE_QUICKSORT -> c34 ENCODE_MAP -> c35 ENCODE_FILTER -> c36 ENCODE_FILTER2 -> c37 APP'(app'(minus, z0), 0) -> c38 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1), APP'(minus, z0)) APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))), APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(quot, app'(app'(minus, z0), z1)), APP'(app'(minus, z0), z1), APP'(minus, z0), APP'(s, z1)) APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1), APP'(le, z0)) APP'(app'(app, nil), z0) -> c45 APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(add, z0), app'(app'(app, z1), z2)), APP'(add, z0), APP'(app'(app, z1), z2), APP'(app, z1)) APP'(app'(low, z0), nil) -> c47 APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_low, app'(app'(le, z1), z0)), z0), APP'(if_low, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(add, z1), app'(app'(low, z0), z2)), APP'(add, z1), APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(high, z0), nil) -> c51 APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_high, app'(app'(le, z1), z0)), z0), APP'(if_high, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2), APP'(high, z0)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(add, z1), app'(app'(high, z0), z2)), APP'(add, z1), APP'(app'(high, z0), z2), APP'(high, z0)) APP'(quicksort, nil) -> c55 APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(app, app'(quicksort, app'(app'(low, z0), z1))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(low, z0), APP'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))), APP'(add, z0), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1), APP'(high, z0)) APP'(app'(map, z0), nil) -> c57 APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)), APP'(add, app'(z0, z1)), APP'(z0, z1), APP'(app'(map, z0), z2), APP'(map, z0)) APP'(app'(filter, z0), nil) -> c59 APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(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) -> c61(APP'(app'(add, z1), app'(app'(filter, z0), z2)), APP'(add, z1), APP'(app'(filter, z0), z2), APP'(filter, z0)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2), APP'(filter, z0)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1), APP'(minus, z0)) APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))), APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(quot, app'(app'(minus, z0), z1)), APP'(app'(minus, z0), z1), APP'(minus, z0), APP'(s, z1)) APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1), APP'(le, z0)) APP'(app'(app, nil), z0) -> c45 APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(add, z0), app'(app'(app, z1), z2)), APP'(add, z0), APP'(app'(app, z1), z2), APP'(app, z1)) APP'(app'(low, z0), nil) -> c47 APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_low, app'(app'(le, z1), z0)), z0), APP'(if_low, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(add, z1), app'(app'(low, z0), z2)), APP'(add, z1), APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(high, z0), nil) -> c51 APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_high, app'(app'(le, z1), z0)), z0), APP'(if_high, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2), APP'(high, z0)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(add, z1), app'(app'(high, z0), z2)), APP'(add, z1), APP'(app'(high, z0), z2), APP'(high, z0)) APP'(quicksort, nil) -> c55 APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(app, app'(quicksort, app'(app'(low, z0), z1))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(low, z0), APP'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))), APP'(add, z0), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1), APP'(high, z0)) APP'(app'(map, z0), nil) -> c57 APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)), APP'(add, app'(z0, z1)), APP'(z0, z1), APP'(app'(map, z0), z2), APP'(map, z0)) APP'(app'(filter, z0), nil) -> c59 APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(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) -> c61(APP'(app'(add, z1), app'(app'(filter, z0), z2)), APP'(add, z1), APP'(app'(filter, z0), z2), APP'(filter, z0)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2), APP'(filter, z0)) K tuples:none Defined Rule Symbols: app'_2, encArg_1, encode_app'_2, encode_minus, encode_0, encode_s, encode_quot, encode_le, encode_true, encode_false, encode_app, encode_nil, encode_add, encode_low, encode_if_low, encode_high, encode_if_high, encode_quicksort, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP'_2, ENCODE_MINUS, ENCODE_0, ENCODE_S, ENCODE_QUOT, ENCODE_LE, ENCODE_TRUE, ENCODE_FALSE, ENCODE_APP, ENCODE_NIL, ENCODE_ADD, ENCODE_LOW, ENCODE_IF_LOW, ENCODE_HIGH, ENCODE_IF_HIGH, ENCODE_QUICKSORT, 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, c16, c17, c18_3, c19_3, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39_2, c40, c41_6, c42, c43, c44_2, c45, c46_4, c47, c48_7, c49_4, c50_2, c51, c52_7, c53_2, c54_4, c55, c56_10, c57, c58_5, c59, c60_5, c61_4, c62_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 36 trailing nodes: ENCODE_TRUE -> c25 ENCODE_LE -> c24 ENCODE_MAP -> c35 ENCODE_NIL -> c28 ENCODE_IF_HIGH -> c33 ENCODE_LOW -> c30 ENCODE_ADD -> c29 ENCARG(filter) -> c16 ENCODE_HIGH -> c32 ENCARG(false) -> c6 ENCARG(add) -> c9 ENCARG(s) -> c2 ENCARG(low) -> c10 ENCODE_FILTER2 -> c37 ENCARG(quot) -> c3 ENCARG(high) -> c12 ENCARG(minus) -> c ENCODE_FILTER -> c36 ENCARG(app) -> c7 ENCARG(filter2) -> c17 ENCARG(if_high) -> c13 ENCARG(nil) -> c8 ENCODE_S -> c22 ENCODE_MINUS -> c20 ENCARG(0) -> c1 ENCODE_IF_LOW -> c31 ENCODE_QUOT -> c23 ENCODE_APP -> c27 ENCODE_QUICKSORT -> c34 ENCARG(if_low) -> c11 ENCODE_0 -> c21 ENCARG(quicksort) -> c14 ENCODE_FALSE -> c26 ENCARG(true) -> c5 ENCARG(le) -> c4 ENCARG(map) -> c15 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, 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)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP'(z0, z1) -> c19(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP'(app'(minus, z0), 0) -> c38 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1), APP'(minus, z0)) APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))), APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(quot, app'(app'(minus, z0), z1)), APP'(app'(minus, z0), z1), APP'(minus, z0), APP'(s, z1)) APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1), APP'(le, z0)) APP'(app'(app, nil), z0) -> c45 APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(add, z0), app'(app'(app, z1), z2)), APP'(add, z0), APP'(app'(app, z1), z2), APP'(app, z1)) APP'(app'(low, z0), nil) -> c47 APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_low, app'(app'(le, z1), z0)), z0), APP'(if_low, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(add, z1), app'(app'(low, z0), z2)), APP'(add, z1), APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(high, z0), nil) -> c51 APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_high, app'(app'(le, z1), z0)), z0), APP'(if_high, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2), APP'(high, z0)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(add, z1), app'(app'(high, z0), z2)), APP'(add, z1), APP'(app'(high, z0), z2), APP'(high, z0)) APP'(quicksort, nil) -> c55 APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(app, app'(quicksort, app'(app'(low, z0), z1))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(low, z0), APP'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))), APP'(add, z0), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1), APP'(high, z0)) APP'(app'(map, z0), nil) -> c57 APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)), APP'(add, app'(z0, z1)), APP'(z0, z1), APP'(app'(map, z0), z2), APP'(map, z0)) APP'(app'(filter, z0), nil) -> c59 APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(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) -> c61(APP'(app'(add, z1), app'(app'(filter, z0), z2)), APP'(add, z1), APP'(app'(filter, z0), z2), APP'(filter, z0)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2), APP'(filter, z0)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1), APP'(minus, z0)) APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))), APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(quot, app'(app'(minus, z0), z1)), APP'(app'(minus, z0), z1), APP'(minus, z0), APP'(s, z1)) APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1), APP'(le, z0)) APP'(app'(app, nil), z0) -> c45 APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(add, z0), app'(app'(app, z1), z2)), APP'(add, z0), APP'(app'(app, z1), z2), APP'(app, z1)) APP'(app'(low, z0), nil) -> c47 APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_low, app'(app'(le, z1), z0)), z0), APP'(if_low, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(add, z1), app'(app'(low, z0), z2)), APP'(add, z1), APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2), APP'(low, z0)) APP'(app'(high, z0), nil) -> c51 APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(if_high, app'(app'(le, z1), z0)), z0), APP'(if_high, app'(app'(le, z1), z0)), APP'(app'(le, z1), z0), APP'(le, z1), APP'(app'(add, z1), z2), APP'(add, z1)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2), APP'(high, z0)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(add, z1), app'(app'(high, z0), z2)), APP'(add, z1), APP'(app'(high, z0), z2), APP'(high, z0)) APP'(quicksort, nil) -> c55 APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(app, app'(quicksort, app'(app'(low, z0), z1))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(low, z0), APP'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))), APP'(add, z0), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1), APP'(high, z0)) APP'(app'(map, z0), nil) -> c57 APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)), APP'(add, app'(z0, z1)), APP'(z0, z1), APP'(app'(map, z0), z2), APP'(map, z0)) APP'(app'(filter, z0), nil) -> c59 APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(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) -> c61(APP'(app'(add, z1), app'(app'(filter, z0), z2)), APP'(add, z1), APP'(app'(filter, z0), z2), APP'(filter, z0)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2), APP'(filter, z0)) K tuples:none Defined Rule Symbols: app'_2, encArg_1, encode_app'_2, encode_minus, encode_0, encode_s, encode_quot, encode_le, encode_true, encode_false, encode_app, encode_nil, encode_add, encode_low, encode_if_low, encode_high, encode_if_high, encode_quicksort, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP'_2, APP'_2 Compound Symbols: c18_3, c19_3, c38, c39_2, c40, c41_6, c42, c43, c44_2, c45, c46_4, c47, c48_7, c49_4, c50_2, c51, c52_7, c53_2, c54_4, c55, c56_10, c57, c58_5, c59, c60_5, c61_4, c62_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 42 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, 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)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP'(z0, z1) -> c19(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) K tuples:none Defined Rule Symbols: app'_2, encArg_1, encode_app'_2, encode_minus, encode_0, encode_s, encode_quot, encode_le, encode_true, encode_false, encode_app, encode_nil, encode_add, encode_low, encode_if_low, encode_high, encode_if_high, encode_quicksort, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP'_2, APP'_2 Compound Symbols: c18_3, c19_3, c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, 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)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCODE_APP'(z0, z1) -> c(ENCARG(z0)) ENCODE_APP'(z0, z1) -> c(ENCARG(z1)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) K tuples:none Defined Rule Symbols: app'_2, encArg_1, encode_app'_2, encode_minus, encode_0, encode_s, encode_quot, encode_le, encode_true, encode_false, encode_app, encode_nil, encode_add, encode_low, encode_if_low, encode_high, encode_if_high, encode_quicksort, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP'_2, ENCODE_APP'_2 Compound Symbols: c18_3, c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_APP'(z0, z1) -> c(ENCARG(z0)) ENCODE_APP'(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort 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_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, 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)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) K tuples:none Defined Rule Symbols: app'_2, encArg_1, encode_app'_2, encode_minus, encode_0, encode_s, encode_quot, encode_le, encode_true, encode_false, encode_app, encode_nil, encode_add, encode_low, encode_if_low, encode_high, encode_if_high, encode_quicksort, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP'_2, ENCODE_APP'_2 Compound Symbols: c18_3, c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_app'(z0, z1) -> app'(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_quot -> quot encode_le -> le encode_true -> true encode_false -> false encode_app -> app encode_nil -> nil encode_add -> add encode_low -> low encode_if_low -> if_low encode_high -> high encode_if_high -> if_high encode_quicksort -> quicksort encode_map -> map encode_filter -> filter encode_filter2 -> filter2 ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, 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)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(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: c18_3, c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(z0, z1)) -> c18(APP'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0), ENCARG(quot)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0), ENCARG(app)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0), ENCARG(add)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0), ENCARG(low)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0), ENCARG(if_low)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0), ENCARG(high)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0), ENCARG(if_high)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0), ENCARG(quicksort)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(minus, x1)) -> c18(APP'(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(APP'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(APP'(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(APP'(quot, encArg(x1)), ENCARG(quot), ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(APP'(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(APP'(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(APP'(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(APP'(app, encArg(x1)), ENCARG(app), ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(APP'(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(APP'(add, encArg(x1)), ENCARG(add), ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(APP'(low, encArg(x1)), ENCARG(low), ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(APP'(if_low, encArg(x1)), ENCARG(if_low), ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(APP'(high, encArg(x1)), ENCARG(high), ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(APP'(if_high, encArg(x1)), ENCARG(if_high), ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(quicksort), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(APP'(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(APP'(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(APP'(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0), ENCARG(quot)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0), ENCARG(app)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0), ENCARG(add)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0), ENCARG(low)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0), ENCARG(if_low)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0), ENCARG(high)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0), ENCARG(if_high)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0), ENCARG(quicksort)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(minus, x1)) -> c18(APP'(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(APP'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(APP'(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(APP'(quot, encArg(x1)), ENCARG(quot), ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(APP'(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(APP'(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(APP'(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(APP'(app, encArg(x1)), ENCARG(app), ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(APP'(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(APP'(add, encArg(x1)), ENCARG(add), ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(APP'(low, encArg(x1)), ENCARG(low), ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(APP'(if_low, encArg(x1)), ENCARG(if_low), ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(APP'(high, encArg(x1)), ENCARG(high), ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(APP'(if_high, encArg(x1)), ENCARG(if_high), ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(quicksort), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(APP'(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(APP'(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(APP'(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1, c18_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 53 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c41_2, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP'(app'(quot, app'(s, z0)), app'(s, z1)) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)), APP'(app'(minus, z0), z1)) by APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) K tuples:none Defined Rule Symbols: encArg_1, app'_2 Defined Pair Symbols: APP'_2, ENCODE_APP'_2, ENCARG_1 Compound Symbols: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c48_2, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP'(app'(low, z0), app'(app'(add, z1), z2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) by APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) K tuples:none Defined Rule Symbols: encArg_1, app'_2 Defined Pair Symbols: APP'_2, ENCODE_APP'_2, ENCARG_1 Compound Symbols: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c52_2, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2, c48_2 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP'(app'(high, z0), app'(app'(add, z1), z2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)), APP'(app'(le, z1), z0)) by APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) K tuples:none Defined Rule Symbols: encArg_1, app'_2 Defined Pair Symbols: APP'_2, ENCODE_APP'_2, ENCARG_1 Compound Symbols: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c56_5, c58_2, c60_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP'(quicksort, app'(app'(add, z0), z1)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))), APP'(quicksort, app'(app'(low, z0), z1)), APP'(app'(low, z0), z1), APP'(quicksort, app'(app'(high, z0), z1)), APP'(app'(high, z0), z1)) by APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) K tuples:none Defined Rule Symbols: encArg_1, app'_2 Defined Pair Symbols: APP'_2, ENCODE_APP'_2, ENCARG_1 Compound Symbols: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c60_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP'(app'(filter, z0), app'(app'(add, z1), z2)) -> c60(APP'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2), APP'(z0, z1)) by APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(app'(app'(filter2, 0), app'(quot, 0)), app'(s, z0)), x2), APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)))), app'(quot, app'(s, z0))), app'(s, z1)), x2), APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z0), app'(app'(app, z1), z2))), app'(app, app'(app'(add, z0), z1))), z2), x2), APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(low, z0)), nil), x2), APP'(app'(low, z0), nil)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(low, z0), z2))), app'(app'(if_low, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(high, z0)), nil), x2), APP'(app'(high, z0), nil)) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(high, z0), z2))), app'(app'(if_high, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), quicksort), nil), x2), APP'(quicksort, nil)) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(map, z0)), nil), x2), APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2))), app'(map, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(filter, z0)), nil), x2), APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, 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'(add, z2), x2)) -> c60(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)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(app'(app'(filter2, 0), app'(quot, 0)), app'(s, z0)), x2), APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)))), app'(quot, app'(s, z0))), app'(s, z1)), x2), APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z0), app'(app'(app, z1), z2))), app'(app, app'(app'(add, z0), z1))), z2), x2), APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(low, z0)), nil), x2), APP'(app'(low, z0), nil)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(low, z0), z2))), app'(app'(if_low, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(high, z0)), nil), x2), APP'(app'(high, z0), nil)) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(high, z0), z2))), app'(app'(if_high, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), quicksort), nil), x2), APP'(quicksort, nil)) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(map, z0)), nil), x2), APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2))), app'(map, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(filter, z0)), nil), x2), APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, 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'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(app'(app'(filter2, 0), app'(quot, 0)), app'(s, z0)), x2), APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1)))), app'(quot, app'(s, z0))), app'(s, z1)), x2), APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z0), app'(app'(app, z1), z2))), app'(app, app'(app'(add, z0), z1))), z2), x2), APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(low, z0)), nil), x2), APP'(app'(low, z0), nil)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(low, z0), z2))), app'(app'(if_low, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(high, z0)), nil), x2), APP'(app'(high, z0), nil)) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, z1), app'(app'(high, z0), z2))), app'(app'(if_high, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), quicksort), nil), x2), APP'(quicksort, nil)) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(map, z0)), nil), x2), APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2))), app'(map, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(app'(app'(filter2, nil), app'(filter, z0)), nil), x2), APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(add, 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'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP'(z0, z1) -> c(APP'(encArg(z0), encArg(z1))) by ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(minus, x1) -> c(APP'(minus, encArg(x1))) ENCODE_APP'(0, x1) -> c(APP'(0, encArg(x1))) ENCODE_APP'(s, x1) -> c(APP'(s, encArg(x1))) ENCODE_APP'(quot, x1) -> c(APP'(quot, encArg(x1))) ENCODE_APP'(le, x1) -> c(APP'(le, encArg(x1))) ENCODE_APP'(true, x1) -> c(APP'(true, encArg(x1))) ENCODE_APP'(false, x1) -> c(APP'(false, encArg(x1))) ENCODE_APP'(app, x1) -> c(APP'(app, encArg(x1))) ENCODE_APP'(nil, x1) -> c(APP'(nil, encArg(x1))) ENCODE_APP'(add, x1) -> c(APP'(add, encArg(x1))) ENCODE_APP'(low, x1) -> c(APP'(low, encArg(x1))) ENCODE_APP'(if_low, x1) -> c(APP'(if_low, encArg(x1))) ENCODE_APP'(high, x1) -> c(APP'(high, encArg(x1))) ENCODE_APP'(if_high, x1) -> c(APP'(if_high, encArg(x1))) ENCODE_APP'(quicksort, x1) -> c(APP'(quicksort, 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))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(minus, x1) -> c(APP'(minus, encArg(x1))) ENCODE_APP'(0, x1) -> c(APP'(0, encArg(x1))) ENCODE_APP'(s, x1) -> c(APP'(s, encArg(x1))) ENCODE_APP'(quot, x1) -> c(APP'(quot, encArg(x1))) ENCODE_APP'(le, x1) -> c(APP'(le, encArg(x1))) ENCODE_APP'(true, x1) -> c(APP'(true, encArg(x1))) ENCODE_APP'(false, x1) -> c(APP'(false, encArg(x1))) ENCODE_APP'(app, x1) -> c(APP'(app, encArg(x1))) ENCODE_APP'(nil, x1) -> c(APP'(nil, encArg(x1))) ENCODE_APP'(add, x1) -> c(APP'(add, encArg(x1))) ENCODE_APP'(low, x1) -> c(APP'(low, encArg(x1))) ENCODE_APP'(if_low, x1) -> c(APP'(if_low, encArg(x1))) ENCODE_APP'(high, x1) -> c(APP'(high, encArg(x1))) ENCODE_APP'(if_high, x1) -> c(APP'(if_high, encArg(x1))) ENCODE_APP'(quicksort, x1) -> c(APP'(quicksort, 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'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing nodes: ENCODE_APP'(add, x1) -> c(APP'(add, encArg(x1))) ENCODE_APP'(low, x1) -> c(APP'(low, encArg(x1))) ENCODE_APP'(high, x1) -> c(APP'(high, encArg(x1))) ENCODE_APP'(true, x1) -> c(APP'(true, encArg(x1))) ENCODE_APP'(if_low, x1) -> c(APP'(if_low, encArg(x1))) ENCODE_APP'(app, x1) -> c(APP'(app, encArg(x1))) ENCODE_APP'(nil, x1) -> c(APP'(nil, encArg(x1))) ENCODE_APP'(s, x1) -> c(APP'(s, encArg(x1))) ENCODE_APP'(filter, x1) -> c(APP'(filter, encArg(x1))) ENCODE_APP'(minus, x1) -> c(APP'(minus, encArg(x1))) ENCODE_APP'(quot, x1) -> c(APP'(quot, encArg(x1))) ENCODE_APP'(filter2, x1) -> c(APP'(filter2, encArg(x1))) ENCODE_APP'(map, x1) -> c(APP'(map, encArg(x1))) ENCODE_APP'(le, x1) -> c(APP'(le, encArg(x1))) ENCODE_APP'(if_high, x1) -> c(APP'(if_high, encArg(x1))) ENCODE_APP'(false, x1) -> c(APP'(false, encArg(x1))) ENCODE_APP'(0, x1) -> c(APP'(0, encArg(x1))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, cons_app'(z0, z1))) -> c18(APP'(encArg(x0), app'(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app'(z0, z1))) by ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(APP'(encArg(x0), app'(app'(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app'(cons_app'(z0, z1), x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(APP'(minus, app'(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(APP'(0, app'(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(APP'(s, app'(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(APP'(quot, app'(encArg(x1), encArg(x2))), ENCARG(quot), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(APP'(le, app'(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(APP'(true, app'(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(APP'(false, app'(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(APP'(app, app'(encArg(x1), encArg(x2))), ENCARG(app), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(APP'(nil, app'(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(APP'(add, app'(encArg(x1), encArg(x2))), ENCARG(add), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(APP'(low, app'(encArg(x1), encArg(x2))), ENCARG(low), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(APP'(if_low, app'(encArg(x1), encArg(x2))), ENCARG(if_low), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(APP'(high, app'(encArg(x1), encArg(x2))), ENCARG(high), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(APP'(if_high, app'(encArg(x1), encArg(x2))), ENCARG(if_high), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(quicksort), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(APP'(map, app'(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(APP'(filter, app'(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(APP'(encArg(x0), app'(app'(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app'(cons_app'(z0, z1), x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(APP'(minus, app'(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(APP'(0, app'(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(APP'(s, app'(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(APP'(quot, app'(encArg(x1), encArg(x2))), ENCARG(quot), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(APP'(le, app'(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(APP'(true, app'(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(APP'(false, app'(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(APP'(app, app'(encArg(x1), encArg(x2))), ENCARG(app), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(APP'(nil, app'(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(APP'(add, app'(encArg(x1), encArg(x2))), ENCARG(add), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(APP'(low, app'(encArg(x1), encArg(x2))), ENCARG(low), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(APP'(if_low, app'(encArg(x1), encArg(x2))), ENCARG(if_low), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(APP'(high, app'(encArg(x1), encArg(x2))), ENCARG(high), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(APP'(if_high, app'(encArg(x1), encArg(x2))), ENCARG(if_high), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(quicksort), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(APP'(map, app'(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(APP'(filter, app'(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 35 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_3, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(cons_app'(z0, z1), x1)) -> c18(APP'(app'(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app'(z0, z1)), ENCARG(x1)) by ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1)), ENCARG(minus)) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1)), ENCARG(0)) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1)), ENCARG(s)) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1)), ENCARG(quot)) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1)), ENCARG(le)) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1)), ENCARG(true)) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1)), ENCARG(false)) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1)), ENCARG(app)) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1)), ENCARG(nil)) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1)), ENCARG(add)) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1)), ENCARG(low)) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1)), ENCARG(if_low)) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1)), ENCARG(high)) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1)), ENCARG(if_high)) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1)), ENCARG(quicksort)) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1)), ENCARG(map)) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1)), ENCARG(filter)) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(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))) -> c18(APP'(app'(encArg(x0), encArg(x1)), app'(encArg(z0), encArg(z1))), ENCARG(cons_app'(x0, x1)), ENCARG(cons_app'(z0, z1))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(APP'(app'(0, encArg(x1)), encArg(x2)), ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(APP'(app'(s, encArg(x1)), encArg(x2)), ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(APP'(app'(true, encArg(x1)), encArg(x2)), ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(APP'(app'(false, encArg(x1)), encArg(x2)), ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(APP'(app'(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(APP'(app'(add, encArg(x1)), encArg(x2)), ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(APP'(app'(if_low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(APP'(app'(if_high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(APP'(app'(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app'(filter, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1)), ENCARG(minus)) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1)), ENCARG(0)) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1)), ENCARG(s)) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1)), ENCARG(quot)) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1)), ENCARG(le)) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1)), ENCARG(true)) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1)), ENCARG(false)) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1)), ENCARG(app)) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1)), ENCARG(nil)) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1)), ENCARG(add)) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1)), ENCARG(low)) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1)), ENCARG(if_low)) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1)), ENCARG(high)) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1)), ENCARG(if_high)) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1)), ENCARG(quicksort)) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1)), ENCARG(map)) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1)), ENCARG(filter)) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1)), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(APP'(app'(0, encArg(x1)), encArg(x2)), ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(APP'(app'(s, encArg(x1)), encArg(x2)), ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(APP'(app'(true, encArg(x1)), encArg(x2)), ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(APP'(app'(false, encArg(x1)), encArg(x2)), ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(APP'(app'(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(APP'(app'(add, encArg(x1)), encArg(x2)), ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(APP'(app'(if_low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(APP'(app'(if_high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(APP'(app'(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app'(filter, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 27 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, minus)) -> c18(APP'(encArg(x0), minus), ENCARG(x0)) by ENCARG(cons_app'(minus, minus)) -> c18(APP'(minus, minus), ENCARG(minus)) ENCARG(cons_app'(0, minus)) -> c18(APP'(0, minus), ENCARG(0)) ENCARG(cons_app'(s, minus)) -> c18(APP'(s, minus), ENCARG(s)) ENCARG(cons_app'(quot, minus)) -> c18(APP'(quot, minus), ENCARG(quot)) ENCARG(cons_app'(le, minus)) -> c18(APP'(le, minus), ENCARG(le)) ENCARG(cons_app'(true, minus)) -> c18(APP'(true, minus), ENCARG(true)) ENCARG(cons_app'(false, minus)) -> c18(APP'(false, minus), ENCARG(false)) ENCARG(cons_app'(app, minus)) -> c18(APP'(app, minus), ENCARG(app)) ENCARG(cons_app'(nil, minus)) -> c18(APP'(nil, minus), ENCARG(nil)) ENCARG(cons_app'(add, minus)) -> c18(APP'(add, minus), ENCARG(add)) ENCARG(cons_app'(low, minus)) -> c18(APP'(low, minus), ENCARG(low)) ENCARG(cons_app'(if_low, minus)) -> c18(APP'(if_low, minus), ENCARG(if_low)) ENCARG(cons_app'(high, minus)) -> c18(APP'(high, minus), ENCARG(high)) ENCARG(cons_app'(if_high, minus)) -> c18(APP'(if_high, minus), ENCARG(if_high)) ENCARG(cons_app'(quicksort, minus)) -> c18(APP'(quicksort, minus), ENCARG(quicksort)) ENCARG(cons_app'(map, minus)) -> c18(APP'(map, minus), ENCARG(map)) ENCARG(cons_app'(filter, minus)) -> c18(APP'(filter, minus), ENCARG(filter)) ENCARG(cons_app'(filter2, minus)) -> c18(APP'(filter2, minus), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), minus)) -> c18(APP'(app'(encArg(z0), encArg(z1)), minus), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, minus)) -> c18(APP'(minus, minus), ENCARG(minus)) ENCARG(cons_app'(0, minus)) -> c18(APP'(0, minus), ENCARG(0)) ENCARG(cons_app'(s, minus)) -> c18(APP'(s, minus), ENCARG(s)) ENCARG(cons_app'(quot, minus)) -> c18(APP'(quot, minus), ENCARG(quot)) ENCARG(cons_app'(le, minus)) -> c18(APP'(le, minus), ENCARG(le)) ENCARG(cons_app'(true, minus)) -> c18(APP'(true, minus), ENCARG(true)) ENCARG(cons_app'(false, minus)) -> c18(APP'(false, minus), ENCARG(false)) ENCARG(cons_app'(app, minus)) -> c18(APP'(app, minus), ENCARG(app)) ENCARG(cons_app'(nil, minus)) -> c18(APP'(nil, minus), ENCARG(nil)) ENCARG(cons_app'(add, minus)) -> c18(APP'(add, minus), ENCARG(add)) ENCARG(cons_app'(low, minus)) -> c18(APP'(low, minus), ENCARG(low)) ENCARG(cons_app'(if_low, minus)) -> c18(APP'(if_low, minus), ENCARG(if_low)) ENCARG(cons_app'(high, minus)) -> c18(APP'(high, minus), ENCARG(high)) ENCARG(cons_app'(if_high, minus)) -> c18(APP'(if_high, minus), ENCARG(if_high)) ENCARG(cons_app'(quicksort, minus)) -> c18(APP'(quicksort, minus), ENCARG(quicksort)) ENCARG(cons_app'(map, minus)) -> c18(APP'(map, minus), ENCARG(map)) ENCARG(cons_app'(filter, minus)) -> c18(APP'(filter, minus), ENCARG(filter)) ENCARG(cons_app'(filter2, minus)) -> c18(APP'(filter2, minus), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(if_high, minus)) -> c18(APP'(if_high, minus), ENCARG(if_high)) ENCARG(cons_app'(if_low, minus)) -> c18(APP'(if_low, minus), ENCARG(if_low)) ENCARG(cons_app'(false, minus)) -> c18(APP'(false, minus), ENCARG(false)) ENCARG(cons_app'(nil, minus)) -> c18(APP'(nil, minus), ENCARG(nil)) ENCARG(cons_app'(app, minus)) -> c18(APP'(app, minus), ENCARG(app)) ENCARG(cons_app'(quot, minus)) -> c18(APP'(quot, minus), ENCARG(quot)) ENCARG(cons_app'(low, minus)) -> c18(APP'(low, minus), ENCARG(low)) ENCARG(cons_app'(map, minus)) -> c18(APP'(map, minus), ENCARG(map)) ENCARG(cons_app'(quicksort, minus)) -> c18(APP'(quicksort, minus), ENCARG(quicksort)) ENCARG(cons_app'(0, minus)) -> c18(APP'(0, minus), ENCARG(0)) ENCARG(cons_app'(true, minus)) -> c18(APP'(true, minus), ENCARG(true)) ENCARG(cons_app'(s, minus)) -> c18(APP'(s, minus), ENCARG(s)) ENCARG(cons_app'(add, minus)) -> c18(APP'(add, minus), ENCARG(add)) ENCARG(cons_app'(high, minus)) -> c18(APP'(high, minus), ENCARG(high)) ENCARG(cons_app'(minus, minus)) -> c18(APP'(minus, minus), ENCARG(minus)) ENCARG(cons_app'(filter2, minus)) -> c18(APP'(filter2, minus), ENCARG(filter2)) ENCARG(cons_app'(filter, minus)) -> c18(APP'(filter, minus), ENCARG(filter)) ENCARG(cons_app'(le, minus)) -> c18(APP'(le, minus), ENCARG(le)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, 0)) -> c18(APP'(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_app'(minus, 0)) -> c18(APP'(minus, 0), ENCARG(minus)) ENCARG(cons_app'(0, 0)) -> c18(APP'(0, 0), ENCARG(0)) ENCARG(cons_app'(s, 0)) -> c18(APP'(s, 0), ENCARG(s)) ENCARG(cons_app'(quot, 0)) -> c18(APP'(quot, 0), ENCARG(quot)) ENCARG(cons_app'(le, 0)) -> c18(APP'(le, 0), ENCARG(le)) ENCARG(cons_app'(true, 0)) -> c18(APP'(true, 0), ENCARG(true)) ENCARG(cons_app'(false, 0)) -> c18(APP'(false, 0), ENCARG(false)) ENCARG(cons_app'(app, 0)) -> c18(APP'(app, 0), ENCARG(app)) ENCARG(cons_app'(nil, 0)) -> c18(APP'(nil, 0), ENCARG(nil)) ENCARG(cons_app'(add, 0)) -> c18(APP'(add, 0), ENCARG(add)) ENCARG(cons_app'(low, 0)) -> c18(APP'(low, 0), ENCARG(low)) ENCARG(cons_app'(if_low, 0)) -> c18(APP'(if_low, 0), ENCARG(if_low)) ENCARG(cons_app'(high, 0)) -> c18(APP'(high, 0), ENCARG(high)) ENCARG(cons_app'(if_high, 0)) -> c18(APP'(if_high, 0), ENCARG(if_high)) ENCARG(cons_app'(quicksort, 0)) -> c18(APP'(quicksort, 0), ENCARG(quicksort)) ENCARG(cons_app'(map, 0)) -> c18(APP'(map, 0), ENCARG(map)) ENCARG(cons_app'(filter, 0)) -> c18(APP'(filter, 0), ENCARG(filter)) ENCARG(cons_app'(filter2, 0)) -> c18(APP'(filter2, 0), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), 0)) -> c18(APP'(app'(encArg(z0), encArg(z1)), 0), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, 0)) -> c18(APP'(minus, 0), ENCARG(minus)) ENCARG(cons_app'(0, 0)) -> c18(APP'(0, 0), ENCARG(0)) ENCARG(cons_app'(s, 0)) -> c18(APP'(s, 0), ENCARG(s)) ENCARG(cons_app'(quot, 0)) -> c18(APP'(quot, 0), ENCARG(quot)) ENCARG(cons_app'(le, 0)) -> c18(APP'(le, 0), ENCARG(le)) ENCARG(cons_app'(true, 0)) -> c18(APP'(true, 0), ENCARG(true)) ENCARG(cons_app'(false, 0)) -> c18(APP'(false, 0), ENCARG(false)) ENCARG(cons_app'(app, 0)) -> c18(APP'(app, 0), ENCARG(app)) ENCARG(cons_app'(nil, 0)) -> c18(APP'(nil, 0), ENCARG(nil)) ENCARG(cons_app'(add, 0)) -> c18(APP'(add, 0), ENCARG(add)) ENCARG(cons_app'(low, 0)) -> c18(APP'(low, 0), ENCARG(low)) ENCARG(cons_app'(if_low, 0)) -> c18(APP'(if_low, 0), ENCARG(if_low)) ENCARG(cons_app'(high, 0)) -> c18(APP'(high, 0), ENCARG(high)) ENCARG(cons_app'(if_high, 0)) -> c18(APP'(if_high, 0), ENCARG(if_high)) ENCARG(cons_app'(quicksort, 0)) -> c18(APP'(quicksort, 0), ENCARG(quicksort)) ENCARG(cons_app'(map, 0)) -> c18(APP'(map, 0), ENCARG(map)) ENCARG(cons_app'(filter, 0)) -> c18(APP'(filter, 0), ENCARG(filter)) ENCARG(cons_app'(filter2, 0)) -> c18(APP'(filter2, 0), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(filter, 0)) -> c18(APP'(filter, 0), ENCARG(filter)) ENCARG(cons_app'(if_high, 0)) -> c18(APP'(if_high, 0), ENCARG(if_high)) ENCARG(cons_app'(0, 0)) -> c18(APP'(0, 0), ENCARG(0)) ENCARG(cons_app'(filter2, 0)) -> c18(APP'(filter2, 0), ENCARG(filter2)) ENCARG(cons_app'(app, 0)) -> c18(APP'(app, 0), ENCARG(app)) ENCARG(cons_app'(quot, 0)) -> c18(APP'(quot, 0), ENCARG(quot)) ENCARG(cons_app'(s, 0)) -> c18(APP'(s, 0), ENCARG(s)) ENCARG(cons_app'(false, 0)) -> c18(APP'(false, 0), ENCARG(false)) ENCARG(cons_app'(minus, 0)) -> c18(APP'(minus, 0), ENCARG(minus)) ENCARG(cons_app'(low, 0)) -> c18(APP'(low, 0), ENCARG(low)) ENCARG(cons_app'(le, 0)) -> c18(APP'(le, 0), ENCARG(le)) ENCARG(cons_app'(quicksort, 0)) -> c18(APP'(quicksort, 0), ENCARG(quicksort)) ENCARG(cons_app'(high, 0)) -> c18(APP'(high, 0), ENCARG(high)) ENCARG(cons_app'(nil, 0)) -> c18(APP'(nil, 0), ENCARG(nil)) ENCARG(cons_app'(map, 0)) -> c18(APP'(map, 0), ENCARG(map)) ENCARG(cons_app'(if_low, 0)) -> c18(APP'(if_low, 0), ENCARG(if_low)) ENCARG(cons_app'(true, 0)) -> c18(APP'(true, 0), ENCARG(true)) ENCARG(cons_app'(add, 0)) -> c18(APP'(add, 0), ENCARG(add)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, s)) -> c18(APP'(encArg(x0), s), ENCARG(x0)) by ENCARG(cons_app'(minus, s)) -> c18(APP'(minus, s), ENCARG(minus)) ENCARG(cons_app'(0, s)) -> c18(APP'(0, s), ENCARG(0)) ENCARG(cons_app'(s, s)) -> c18(APP'(s, s), ENCARG(s)) ENCARG(cons_app'(quot, s)) -> c18(APP'(quot, s), ENCARG(quot)) ENCARG(cons_app'(le, s)) -> c18(APP'(le, s), ENCARG(le)) ENCARG(cons_app'(true, s)) -> c18(APP'(true, s), ENCARG(true)) ENCARG(cons_app'(false, s)) -> c18(APP'(false, s), ENCARG(false)) ENCARG(cons_app'(app, s)) -> c18(APP'(app, s), ENCARG(app)) ENCARG(cons_app'(nil, s)) -> c18(APP'(nil, s), ENCARG(nil)) ENCARG(cons_app'(add, s)) -> c18(APP'(add, s), ENCARG(add)) ENCARG(cons_app'(low, s)) -> c18(APP'(low, s), ENCARG(low)) ENCARG(cons_app'(if_low, s)) -> c18(APP'(if_low, s), ENCARG(if_low)) ENCARG(cons_app'(high, s)) -> c18(APP'(high, s), ENCARG(high)) ENCARG(cons_app'(if_high, s)) -> c18(APP'(if_high, s), ENCARG(if_high)) ENCARG(cons_app'(quicksort, s)) -> c18(APP'(quicksort, s), ENCARG(quicksort)) ENCARG(cons_app'(map, s)) -> c18(APP'(map, s), ENCARG(map)) ENCARG(cons_app'(filter, s)) -> c18(APP'(filter, s), ENCARG(filter)) ENCARG(cons_app'(filter2, s)) -> c18(APP'(filter2, s), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), s)) -> c18(APP'(app'(encArg(z0), encArg(z1)), s), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, s)) -> c18(APP'(minus, s), ENCARG(minus)) ENCARG(cons_app'(0, s)) -> c18(APP'(0, s), ENCARG(0)) ENCARG(cons_app'(s, s)) -> c18(APP'(s, s), ENCARG(s)) ENCARG(cons_app'(quot, s)) -> c18(APP'(quot, s), ENCARG(quot)) ENCARG(cons_app'(le, s)) -> c18(APP'(le, s), ENCARG(le)) ENCARG(cons_app'(true, s)) -> c18(APP'(true, s), ENCARG(true)) ENCARG(cons_app'(false, s)) -> c18(APP'(false, s), ENCARG(false)) ENCARG(cons_app'(app, s)) -> c18(APP'(app, s), ENCARG(app)) ENCARG(cons_app'(nil, s)) -> c18(APP'(nil, s), ENCARG(nil)) ENCARG(cons_app'(add, s)) -> c18(APP'(add, s), ENCARG(add)) ENCARG(cons_app'(low, s)) -> c18(APP'(low, s), ENCARG(low)) ENCARG(cons_app'(if_low, s)) -> c18(APP'(if_low, s), ENCARG(if_low)) ENCARG(cons_app'(high, s)) -> c18(APP'(high, s), ENCARG(high)) ENCARG(cons_app'(if_high, s)) -> c18(APP'(if_high, s), ENCARG(if_high)) ENCARG(cons_app'(quicksort, s)) -> c18(APP'(quicksort, s), ENCARG(quicksort)) ENCARG(cons_app'(map, s)) -> c18(APP'(map, s), ENCARG(map)) ENCARG(cons_app'(filter, s)) -> c18(APP'(filter, s), ENCARG(filter)) ENCARG(cons_app'(filter2, s)) -> c18(APP'(filter2, s), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(filter2, s)) -> c18(APP'(filter2, s), ENCARG(filter2)) ENCARG(cons_app'(true, s)) -> c18(APP'(true, s), ENCARG(true)) ENCARG(cons_app'(quicksort, s)) -> c18(APP'(quicksort, s), ENCARG(quicksort)) ENCARG(cons_app'(nil, s)) -> c18(APP'(nil, s), ENCARG(nil)) ENCARG(cons_app'(if_high, s)) -> c18(APP'(if_high, s), ENCARG(if_high)) ENCARG(cons_app'(le, s)) -> c18(APP'(le, s), ENCARG(le)) ENCARG(cons_app'(map, s)) -> c18(APP'(map, s), ENCARG(map)) ENCARG(cons_app'(0, s)) -> c18(APP'(0, s), ENCARG(0)) ENCARG(cons_app'(low, s)) -> c18(APP'(low, s), ENCARG(low)) ENCARG(cons_app'(s, s)) -> c18(APP'(s, s), ENCARG(s)) ENCARG(cons_app'(app, s)) -> c18(APP'(app, s), ENCARG(app)) ENCARG(cons_app'(quot, s)) -> c18(APP'(quot, s), ENCARG(quot)) ENCARG(cons_app'(filter, s)) -> c18(APP'(filter, s), ENCARG(filter)) ENCARG(cons_app'(high, s)) -> c18(APP'(high, s), ENCARG(high)) ENCARG(cons_app'(add, s)) -> c18(APP'(add, s), ENCARG(add)) ENCARG(cons_app'(minus, s)) -> c18(APP'(minus, s), ENCARG(minus)) ENCARG(cons_app'(if_low, s)) -> c18(APP'(if_low, s), ENCARG(if_low)) ENCARG(cons_app'(false, s)) -> c18(APP'(false, s), ENCARG(false)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, quot)) -> c18(APP'(encArg(x0), quot), ENCARG(x0)) by ENCARG(cons_app'(minus, quot)) -> c18(APP'(minus, quot), ENCARG(minus)) ENCARG(cons_app'(0, quot)) -> c18(APP'(0, quot), ENCARG(0)) ENCARG(cons_app'(s, quot)) -> c18(APP'(s, quot), ENCARG(s)) ENCARG(cons_app'(quot, quot)) -> c18(APP'(quot, quot), ENCARG(quot)) ENCARG(cons_app'(le, quot)) -> c18(APP'(le, quot), ENCARG(le)) ENCARG(cons_app'(true, quot)) -> c18(APP'(true, quot), ENCARG(true)) ENCARG(cons_app'(false, quot)) -> c18(APP'(false, quot), ENCARG(false)) ENCARG(cons_app'(app, quot)) -> c18(APP'(app, quot), ENCARG(app)) ENCARG(cons_app'(nil, quot)) -> c18(APP'(nil, quot), ENCARG(nil)) ENCARG(cons_app'(add, quot)) -> c18(APP'(add, quot), ENCARG(add)) ENCARG(cons_app'(low, quot)) -> c18(APP'(low, quot), ENCARG(low)) ENCARG(cons_app'(if_low, quot)) -> c18(APP'(if_low, quot), ENCARG(if_low)) ENCARG(cons_app'(high, quot)) -> c18(APP'(high, quot), ENCARG(high)) ENCARG(cons_app'(if_high, quot)) -> c18(APP'(if_high, quot), ENCARG(if_high)) ENCARG(cons_app'(quicksort, quot)) -> c18(APP'(quicksort, quot), ENCARG(quicksort)) ENCARG(cons_app'(map, quot)) -> c18(APP'(map, quot), ENCARG(map)) ENCARG(cons_app'(filter, quot)) -> c18(APP'(filter, quot), ENCARG(filter)) ENCARG(cons_app'(filter2, quot)) -> c18(APP'(filter2, quot), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), quot)) -> c18(APP'(app'(encArg(z0), encArg(z1)), quot), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, quot)) -> c18(APP'(minus, quot), ENCARG(minus)) ENCARG(cons_app'(0, quot)) -> c18(APP'(0, quot), ENCARG(0)) ENCARG(cons_app'(s, quot)) -> c18(APP'(s, quot), ENCARG(s)) ENCARG(cons_app'(quot, quot)) -> c18(APP'(quot, quot), ENCARG(quot)) ENCARG(cons_app'(le, quot)) -> c18(APP'(le, quot), ENCARG(le)) ENCARG(cons_app'(true, quot)) -> c18(APP'(true, quot), ENCARG(true)) ENCARG(cons_app'(false, quot)) -> c18(APP'(false, quot), ENCARG(false)) ENCARG(cons_app'(app, quot)) -> c18(APP'(app, quot), ENCARG(app)) ENCARG(cons_app'(nil, quot)) -> c18(APP'(nil, quot), ENCARG(nil)) ENCARG(cons_app'(add, quot)) -> c18(APP'(add, quot), ENCARG(add)) ENCARG(cons_app'(low, quot)) -> c18(APP'(low, quot), ENCARG(low)) ENCARG(cons_app'(if_low, quot)) -> c18(APP'(if_low, quot), ENCARG(if_low)) ENCARG(cons_app'(high, quot)) -> c18(APP'(high, quot), ENCARG(high)) ENCARG(cons_app'(if_high, quot)) -> c18(APP'(if_high, quot), ENCARG(if_high)) ENCARG(cons_app'(quicksort, quot)) -> c18(APP'(quicksort, quot), ENCARG(quicksort)) ENCARG(cons_app'(map, quot)) -> c18(APP'(map, quot), ENCARG(map)) ENCARG(cons_app'(filter, quot)) -> c18(APP'(filter, quot), ENCARG(filter)) ENCARG(cons_app'(filter2, quot)) -> c18(APP'(filter2, quot), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(if_low, quot)) -> c18(APP'(if_low, quot), ENCARG(if_low)) ENCARG(cons_app'(if_high, quot)) -> c18(APP'(if_high, quot), ENCARG(if_high)) ENCARG(cons_app'(false, quot)) -> c18(APP'(false, quot), ENCARG(false)) ENCARG(cons_app'(nil, quot)) -> c18(APP'(nil, quot), ENCARG(nil)) ENCARG(cons_app'(minus, quot)) -> c18(APP'(minus, quot), ENCARG(minus)) ENCARG(cons_app'(le, quot)) -> c18(APP'(le, quot), ENCARG(le)) ENCARG(cons_app'(true, quot)) -> c18(APP'(true, quot), ENCARG(true)) ENCARG(cons_app'(add, quot)) -> c18(APP'(add, quot), ENCARG(add)) ENCARG(cons_app'(s, quot)) -> c18(APP'(s, quot), ENCARG(s)) ENCARG(cons_app'(filter, quot)) -> c18(APP'(filter, quot), ENCARG(filter)) ENCARG(cons_app'(filter2, quot)) -> c18(APP'(filter2, quot), ENCARG(filter2)) ENCARG(cons_app'(quicksort, quot)) -> c18(APP'(quicksort, quot), ENCARG(quicksort)) ENCARG(cons_app'(map, quot)) -> c18(APP'(map, quot), ENCARG(map)) ENCARG(cons_app'(high, quot)) -> c18(APP'(high, quot), ENCARG(high)) ENCARG(cons_app'(app, quot)) -> c18(APP'(app, quot), ENCARG(app)) ENCARG(cons_app'(quot, quot)) -> c18(APP'(quot, quot), ENCARG(quot)) ENCARG(cons_app'(low, quot)) -> c18(APP'(low, quot), ENCARG(low)) ENCARG(cons_app'(0, quot)) -> c18(APP'(0, quot), ENCARG(0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, le)) -> c18(APP'(encArg(x0), le), ENCARG(x0)) by ENCARG(cons_app'(minus, le)) -> c18(APP'(minus, le), ENCARG(minus)) ENCARG(cons_app'(0, le)) -> c18(APP'(0, le), ENCARG(0)) ENCARG(cons_app'(s, le)) -> c18(APP'(s, le), ENCARG(s)) ENCARG(cons_app'(quot, le)) -> c18(APP'(quot, le), ENCARG(quot)) ENCARG(cons_app'(le, le)) -> c18(APP'(le, le), ENCARG(le)) ENCARG(cons_app'(true, le)) -> c18(APP'(true, le), ENCARG(true)) ENCARG(cons_app'(false, le)) -> c18(APP'(false, le), ENCARG(false)) ENCARG(cons_app'(app, le)) -> c18(APP'(app, le), ENCARG(app)) ENCARG(cons_app'(nil, le)) -> c18(APP'(nil, le), ENCARG(nil)) ENCARG(cons_app'(add, le)) -> c18(APP'(add, le), ENCARG(add)) ENCARG(cons_app'(low, le)) -> c18(APP'(low, le), ENCARG(low)) ENCARG(cons_app'(if_low, le)) -> c18(APP'(if_low, le), ENCARG(if_low)) ENCARG(cons_app'(high, le)) -> c18(APP'(high, le), ENCARG(high)) ENCARG(cons_app'(if_high, le)) -> c18(APP'(if_high, le), ENCARG(if_high)) ENCARG(cons_app'(quicksort, le)) -> c18(APP'(quicksort, le), ENCARG(quicksort)) ENCARG(cons_app'(map, le)) -> c18(APP'(map, le), ENCARG(map)) ENCARG(cons_app'(filter, le)) -> c18(APP'(filter, le), ENCARG(filter)) ENCARG(cons_app'(filter2, le)) -> c18(APP'(filter2, le), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), le)) -> c18(APP'(app'(encArg(z0), encArg(z1)), le), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, le)) -> c18(APP'(minus, le), ENCARG(minus)) ENCARG(cons_app'(0, le)) -> c18(APP'(0, le), ENCARG(0)) ENCARG(cons_app'(s, le)) -> c18(APP'(s, le), ENCARG(s)) ENCARG(cons_app'(quot, le)) -> c18(APP'(quot, le), ENCARG(quot)) ENCARG(cons_app'(le, le)) -> c18(APP'(le, le), ENCARG(le)) ENCARG(cons_app'(true, le)) -> c18(APP'(true, le), ENCARG(true)) ENCARG(cons_app'(false, le)) -> c18(APP'(false, le), ENCARG(false)) ENCARG(cons_app'(app, le)) -> c18(APP'(app, le), ENCARG(app)) ENCARG(cons_app'(nil, le)) -> c18(APP'(nil, le), ENCARG(nil)) ENCARG(cons_app'(add, le)) -> c18(APP'(add, le), ENCARG(add)) ENCARG(cons_app'(low, le)) -> c18(APP'(low, le), ENCARG(low)) ENCARG(cons_app'(if_low, le)) -> c18(APP'(if_low, le), ENCARG(if_low)) ENCARG(cons_app'(high, le)) -> c18(APP'(high, le), ENCARG(high)) ENCARG(cons_app'(if_high, le)) -> c18(APP'(if_high, le), ENCARG(if_high)) ENCARG(cons_app'(quicksort, le)) -> c18(APP'(quicksort, le), ENCARG(quicksort)) ENCARG(cons_app'(map, le)) -> c18(APP'(map, le), ENCARG(map)) ENCARG(cons_app'(filter, le)) -> c18(APP'(filter, le), ENCARG(filter)) ENCARG(cons_app'(filter2, le)) -> c18(APP'(filter2, le), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(map, le)) -> c18(APP'(map, le), ENCARG(map)) ENCARG(cons_app'(filter, le)) -> c18(APP'(filter, le), ENCARG(filter)) ENCARG(cons_app'(high, le)) -> c18(APP'(high, le), ENCARG(high)) ENCARG(cons_app'(minus, le)) -> c18(APP'(minus, le), ENCARG(minus)) ENCARG(cons_app'(true, le)) -> c18(APP'(true, le), ENCARG(true)) ENCARG(cons_app'(quicksort, le)) -> c18(APP'(quicksort, le), ENCARG(quicksort)) ENCARG(cons_app'(s, le)) -> c18(APP'(s, le), ENCARG(s)) ENCARG(cons_app'(if_high, le)) -> c18(APP'(if_high, le), ENCARG(if_high)) ENCARG(cons_app'(le, le)) -> c18(APP'(le, le), ENCARG(le)) ENCARG(cons_app'(add, le)) -> c18(APP'(add, le), ENCARG(add)) ENCARG(cons_app'(filter2, le)) -> c18(APP'(filter2, le), ENCARG(filter2)) ENCARG(cons_app'(0, le)) -> c18(APP'(0, le), ENCARG(0)) ENCARG(cons_app'(if_low, le)) -> c18(APP'(if_low, le), ENCARG(if_low)) ENCARG(cons_app'(nil, le)) -> c18(APP'(nil, le), ENCARG(nil)) ENCARG(cons_app'(app, le)) -> c18(APP'(app, le), ENCARG(app)) ENCARG(cons_app'(false, le)) -> c18(APP'(false, le), ENCARG(false)) ENCARG(cons_app'(quot, le)) -> c18(APP'(quot, le), ENCARG(quot)) ENCARG(cons_app'(low, le)) -> c18(APP'(low, le), ENCARG(low)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, true)) -> c18(APP'(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app'(minus, true)) -> c18(APP'(minus, true), ENCARG(minus)) ENCARG(cons_app'(0, true)) -> c18(APP'(0, true), ENCARG(0)) ENCARG(cons_app'(s, true)) -> c18(APP'(s, true), ENCARG(s)) ENCARG(cons_app'(quot, true)) -> c18(APP'(quot, true), ENCARG(quot)) ENCARG(cons_app'(le, true)) -> c18(APP'(le, true), ENCARG(le)) ENCARG(cons_app'(true, true)) -> c18(APP'(true, true), ENCARG(true)) ENCARG(cons_app'(false, true)) -> c18(APP'(false, true), ENCARG(false)) ENCARG(cons_app'(app, true)) -> c18(APP'(app, true), ENCARG(app)) ENCARG(cons_app'(nil, true)) -> c18(APP'(nil, true), ENCARG(nil)) ENCARG(cons_app'(add, true)) -> c18(APP'(add, true), ENCARG(add)) ENCARG(cons_app'(low, true)) -> c18(APP'(low, true), ENCARG(low)) ENCARG(cons_app'(if_low, true)) -> c18(APP'(if_low, true), ENCARG(if_low)) ENCARG(cons_app'(high, true)) -> c18(APP'(high, true), ENCARG(high)) ENCARG(cons_app'(if_high, true)) -> c18(APP'(if_high, true), ENCARG(if_high)) ENCARG(cons_app'(quicksort, true)) -> c18(APP'(quicksort, true), ENCARG(quicksort)) ENCARG(cons_app'(map, true)) -> c18(APP'(map, true), ENCARG(map)) ENCARG(cons_app'(filter, true)) -> c18(APP'(filter, true), ENCARG(filter)) ENCARG(cons_app'(filter2, true)) -> c18(APP'(filter2, true), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), true)) -> c18(APP'(app'(encArg(z0), encArg(z1)), true), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, true)) -> c18(APP'(minus, true), ENCARG(minus)) ENCARG(cons_app'(0, true)) -> c18(APP'(0, true), ENCARG(0)) ENCARG(cons_app'(s, true)) -> c18(APP'(s, true), ENCARG(s)) ENCARG(cons_app'(quot, true)) -> c18(APP'(quot, true), ENCARG(quot)) ENCARG(cons_app'(le, true)) -> c18(APP'(le, true), ENCARG(le)) ENCARG(cons_app'(true, true)) -> c18(APP'(true, true), ENCARG(true)) ENCARG(cons_app'(false, true)) -> c18(APP'(false, true), ENCARG(false)) ENCARG(cons_app'(app, true)) -> c18(APP'(app, true), ENCARG(app)) ENCARG(cons_app'(nil, true)) -> c18(APP'(nil, true), ENCARG(nil)) ENCARG(cons_app'(add, true)) -> c18(APP'(add, true), ENCARG(add)) ENCARG(cons_app'(low, true)) -> c18(APP'(low, true), ENCARG(low)) ENCARG(cons_app'(if_low, true)) -> c18(APP'(if_low, true), ENCARG(if_low)) ENCARG(cons_app'(high, true)) -> c18(APP'(high, true), ENCARG(high)) ENCARG(cons_app'(if_high, true)) -> c18(APP'(if_high, true), ENCARG(if_high)) ENCARG(cons_app'(quicksort, true)) -> c18(APP'(quicksort, true), ENCARG(quicksort)) ENCARG(cons_app'(map, true)) -> c18(APP'(map, true), ENCARG(map)) ENCARG(cons_app'(filter, true)) -> c18(APP'(filter, true), ENCARG(filter)) ENCARG(cons_app'(filter2, true)) -> c18(APP'(filter2, true), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(nil, true)) -> c18(APP'(nil, true), ENCARG(nil)) ENCARG(cons_app'(false, true)) -> c18(APP'(false, true), ENCARG(false)) ENCARG(cons_app'(true, true)) -> c18(APP'(true, true), ENCARG(true)) ENCARG(cons_app'(s, true)) -> c18(APP'(s, true), ENCARG(s)) ENCARG(cons_app'(map, true)) -> c18(APP'(map, true), ENCARG(map)) ENCARG(cons_app'(filter, true)) -> c18(APP'(filter, true), ENCARG(filter)) ENCARG(cons_app'(0, true)) -> c18(APP'(0, true), ENCARG(0)) ENCARG(cons_app'(app, true)) -> c18(APP'(app, true), ENCARG(app)) ENCARG(cons_app'(quot, true)) -> c18(APP'(quot, true), ENCARG(quot)) ENCARG(cons_app'(minus, true)) -> c18(APP'(minus, true), ENCARG(minus)) ENCARG(cons_app'(if_high, true)) -> c18(APP'(if_high, true), ENCARG(if_high)) ENCARG(cons_app'(high, true)) -> c18(APP'(high, true), ENCARG(high)) ENCARG(cons_app'(if_low, true)) -> c18(APP'(if_low, true), ENCARG(if_low)) ENCARG(cons_app'(filter2, true)) -> c18(APP'(filter2, true), ENCARG(filter2)) ENCARG(cons_app'(add, true)) -> c18(APP'(add, true), ENCARG(add)) ENCARG(cons_app'(quicksort, true)) -> c18(APP'(quicksort, true), ENCARG(quicksort)) ENCARG(cons_app'(low, true)) -> c18(APP'(low, true), ENCARG(low)) ENCARG(cons_app'(le, true)) -> c18(APP'(le, true), ENCARG(le)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, false)) -> c18(APP'(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app'(minus, false)) -> c18(APP'(minus, false), ENCARG(minus)) ENCARG(cons_app'(0, false)) -> c18(APP'(0, false), ENCARG(0)) ENCARG(cons_app'(s, false)) -> c18(APP'(s, false), ENCARG(s)) ENCARG(cons_app'(quot, false)) -> c18(APP'(quot, false), ENCARG(quot)) ENCARG(cons_app'(le, false)) -> c18(APP'(le, false), ENCARG(le)) ENCARG(cons_app'(true, false)) -> c18(APP'(true, false), ENCARG(true)) ENCARG(cons_app'(false, false)) -> c18(APP'(false, false), ENCARG(false)) ENCARG(cons_app'(app, false)) -> c18(APP'(app, false), ENCARG(app)) ENCARG(cons_app'(nil, false)) -> c18(APP'(nil, false), ENCARG(nil)) ENCARG(cons_app'(add, false)) -> c18(APP'(add, false), ENCARG(add)) ENCARG(cons_app'(low, false)) -> c18(APP'(low, false), ENCARG(low)) ENCARG(cons_app'(if_low, false)) -> c18(APP'(if_low, false), ENCARG(if_low)) ENCARG(cons_app'(high, false)) -> c18(APP'(high, false), ENCARG(high)) ENCARG(cons_app'(if_high, false)) -> c18(APP'(if_high, false), ENCARG(if_high)) ENCARG(cons_app'(quicksort, false)) -> c18(APP'(quicksort, false), ENCARG(quicksort)) ENCARG(cons_app'(map, false)) -> c18(APP'(map, false), ENCARG(map)) ENCARG(cons_app'(filter, false)) -> c18(APP'(filter, false), ENCARG(filter)) ENCARG(cons_app'(filter2, false)) -> c18(APP'(filter2, false), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), false)) -> c18(APP'(app'(encArg(z0), encArg(z1)), false), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, false)) -> c18(APP'(minus, false), ENCARG(minus)) ENCARG(cons_app'(0, false)) -> c18(APP'(0, false), ENCARG(0)) ENCARG(cons_app'(s, false)) -> c18(APP'(s, false), ENCARG(s)) ENCARG(cons_app'(quot, false)) -> c18(APP'(quot, false), ENCARG(quot)) ENCARG(cons_app'(le, false)) -> c18(APP'(le, false), ENCARG(le)) ENCARG(cons_app'(true, false)) -> c18(APP'(true, false), ENCARG(true)) ENCARG(cons_app'(false, false)) -> c18(APP'(false, false), ENCARG(false)) ENCARG(cons_app'(app, false)) -> c18(APP'(app, false), ENCARG(app)) ENCARG(cons_app'(nil, false)) -> c18(APP'(nil, false), ENCARG(nil)) ENCARG(cons_app'(add, false)) -> c18(APP'(add, false), ENCARG(add)) ENCARG(cons_app'(low, false)) -> c18(APP'(low, false), ENCARG(low)) ENCARG(cons_app'(if_low, false)) -> c18(APP'(if_low, false), ENCARG(if_low)) ENCARG(cons_app'(high, false)) -> c18(APP'(high, false), ENCARG(high)) ENCARG(cons_app'(if_high, false)) -> c18(APP'(if_high, false), ENCARG(if_high)) ENCARG(cons_app'(quicksort, false)) -> c18(APP'(quicksort, false), ENCARG(quicksort)) ENCARG(cons_app'(map, false)) -> c18(APP'(map, false), ENCARG(map)) ENCARG(cons_app'(filter, false)) -> c18(APP'(filter, false), ENCARG(filter)) ENCARG(cons_app'(filter2, false)) -> c18(APP'(filter2, false), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(high, false)) -> c18(APP'(high, false), ENCARG(high)) ENCARG(cons_app'(false, false)) -> c18(APP'(false, false), ENCARG(false)) ENCARG(cons_app'(filter2, false)) -> c18(APP'(filter2, false), ENCARG(filter2)) ENCARG(cons_app'(quicksort, false)) -> c18(APP'(quicksort, false), ENCARG(quicksort)) ENCARG(cons_app'(if_low, false)) -> c18(APP'(if_low, false), ENCARG(if_low)) ENCARG(cons_app'(if_high, false)) -> c18(APP'(if_high, false), ENCARG(if_high)) ENCARG(cons_app'(low, false)) -> c18(APP'(low, false), ENCARG(low)) ENCARG(cons_app'(filter, false)) -> c18(APP'(filter, false), ENCARG(filter)) ENCARG(cons_app'(s, false)) -> c18(APP'(s, false), ENCARG(s)) ENCARG(cons_app'(app, false)) -> c18(APP'(app, false), ENCARG(app)) ENCARG(cons_app'(quot, false)) -> c18(APP'(quot, false), ENCARG(quot)) ENCARG(cons_app'(true, false)) -> c18(APP'(true, false), ENCARG(true)) ENCARG(cons_app'(map, false)) -> c18(APP'(map, false), ENCARG(map)) ENCARG(cons_app'(nil, false)) -> c18(APP'(nil, false), ENCARG(nil)) ENCARG(cons_app'(le, false)) -> c18(APP'(le, false), ENCARG(le)) ENCARG(cons_app'(add, false)) -> c18(APP'(add, false), ENCARG(add)) ENCARG(cons_app'(0, false)) -> c18(APP'(0, false), ENCARG(0)) ENCARG(cons_app'(minus, false)) -> c18(APP'(minus, false), ENCARG(minus)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, app)) -> c18(APP'(encArg(x0), app), ENCARG(x0)) by ENCARG(cons_app'(minus, app)) -> c18(APP'(minus, app), ENCARG(minus)) ENCARG(cons_app'(0, app)) -> c18(APP'(0, app), ENCARG(0)) ENCARG(cons_app'(s, app)) -> c18(APP'(s, app), ENCARG(s)) ENCARG(cons_app'(quot, app)) -> c18(APP'(quot, app), ENCARG(quot)) ENCARG(cons_app'(le, app)) -> c18(APP'(le, app), ENCARG(le)) ENCARG(cons_app'(true, app)) -> c18(APP'(true, app), ENCARG(true)) ENCARG(cons_app'(false, app)) -> c18(APP'(false, app), ENCARG(false)) ENCARG(cons_app'(app, app)) -> c18(APP'(app, app), ENCARG(app)) ENCARG(cons_app'(nil, app)) -> c18(APP'(nil, app), ENCARG(nil)) ENCARG(cons_app'(add, app)) -> c18(APP'(add, app), ENCARG(add)) ENCARG(cons_app'(low, app)) -> c18(APP'(low, app), ENCARG(low)) ENCARG(cons_app'(if_low, app)) -> c18(APP'(if_low, app), ENCARG(if_low)) ENCARG(cons_app'(high, app)) -> c18(APP'(high, app), ENCARG(high)) ENCARG(cons_app'(if_high, app)) -> c18(APP'(if_high, app), ENCARG(if_high)) ENCARG(cons_app'(quicksort, app)) -> c18(APP'(quicksort, app), ENCARG(quicksort)) ENCARG(cons_app'(map, app)) -> c18(APP'(map, app), ENCARG(map)) ENCARG(cons_app'(filter, app)) -> c18(APP'(filter, app), ENCARG(filter)) ENCARG(cons_app'(filter2, app)) -> c18(APP'(filter2, app), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), app)) -> c18(APP'(app'(encArg(z0), encArg(z1)), app), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, app)) -> c18(APP'(minus, app), ENCARG(minus)) ENCARG(cons_app'(0, app)) -> c18(APP'(0, app), ENCARG(0)) ENCARG(cons_app'(s, app)) -> c18(APP'(s, app), ENCARG(s)) ENCARG(cons_app'(quot, app)) -> c18(APP'(quot, app), ENCARG(quot)) ENCARG(cons_app'(le, app)) -> c18(APP'(le, app), ENCARG(le)) ENCARG(cons_app'(true, app)) -> c18(APP'(true, app), ENCARG(true)) ENCARG(cons_app'(false, app)) -> c18(APP'(false, app), ENCARG(false)) ENCARG(cons_app'(app, app)) -> c18(APP'(app, app), ENCARG(app)) ENCARG(cons_app'(nil, app)) -> c18(APP'(nil, app), ENCARG(nil)) ENCARG(cons_app'(add, app)) -> c18(APP'(add, app), ENCARG(add)) ENCARG(cons_app'(low, app)) -> c18(APP'(low, app), ENCARG(low)) ENCARG(cons_app'(if_low, app)) -> c18(APP'(if_low, app), ENCARG(if_low)) ENCARG(cons_app'(high, app)) -> c18(APP'(high, app), ENCARG(high)) ENCARG(cons_app'(if_high, app)) -> c18(APP'(if_high, app), ENCARG(if_high)) ENCARG(cons_app'(quicksort, app)) -> c18(APP'(quicksort, app), ENCARG(quicksort)) ENCARG(cons_app'(map, app)) -> c18(APP'(map, app), ENCARG(map)) ENCARG(cons_app'(filter, app)) -> c18(APP'(filter, app), ENCARG(filter)) ENCARG(cons_app'(filter2, app)) -> c18(APP'(filter2, app), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app'(false, app)) -> c18(APP'(false, app), ENCARG(false)) ENCARG(cons_app'(minus, app)) -> c18(APP'(minus, app), ENCARG(minus)) ENCARG(cons_app'(high, app)) -> c18(APP'(high, app), ENCARG(high)) ENCARG(cons_app'(filter2, app)) -> c18(APP'(filter2, app), ENCARG(filter2)) ENCARG(cons_app'(low, app)) -> c18(APP'(low, app), ENCARG(low)) ENCARG(cons_app'(le, app)) -> c18(APP'(le, app), ENCARG(le)) ENCARG(cons_app'(s, app)) -> c18(APP'(s, app), ENCARG(s)) ENCARG(cons_app'(true, app)) -> c18(APP'(true, app), ENCARG(true)) ENCARG(cons_app'(map, app)) -> c18(APP'(map, app), ENCARG(map)) ENCARG(cons_app'(if_high, app)) -> c18(APP'(if_high, app), ENCARG(if_high)) ENCARG(cons_app'(if_low, app)) -> c18(APP'(if_low, app), ENCARG(if_low)) ENCARG(cons_app'(add, app)) -> c18(APP'(add, app), ENCARG(add)) ENCARG(cons_app'(filter, app)) -> c18(APP'(filter, app), ENCARG(filter)) ENCARG(cons_app'(quicksort, app)) -> c18(APP'(quicksort, app), ENCARG(quicksort)) ENCARG(cons_app'(0, app)) -> c18(APP'(0, app), ENCARG(0)) ENCARG(cons_app'(nil, app)) -> c18(APP'(nil, app), ENCARG(nil)) ENCARG(cons_app'(app, app)) -> c18(APP'(app, app), ENCARG(app)) ENCARG(cons_app'(quot, app)) -> c18(APP'(quot, app), ENCARG(quot)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app'(x0, nil)) -> c18(APP'(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app'(minus, nil)) -> c18(APP'(minus, nil), ENCARG(minus)) ENCARG(cons_app'(0, nil)) -> c18(APP'(0, nil), ENCARG(0)) ENCARG(cons_app'(s, nil)) -> c18(APP'(s, nil), ENCARG(s)) ENCARG(cons_app'(quot, nil)) -> c18(APP'(quot, nil), ENCARG(quot)) ENCARG(cons_app'(le, nil)) -> c18(APP'(le, nil), ENCARG(le)) ENCARG(cons_app'(true, nil)) -> c18(APP'(true, nil), ENCARG(true)) ENCARG(cons_app'(false, nil)) -> c18(APP'(false, nil), ENCARG(false)) ENCARG(cons_app'(app, nil)) -> c18(APP'(app, nil), ENCARG(app)) ENCARG(cons_app'(nil, nil)) -> c18(APP'(nil, nil), ENCARG(nil)) ENCARG(cons_app'(add, nil)) -> c18(APP'(add, nil), ENCARG(add)) ENCARG(cons_app'(low, nil)) -> c18(APP'(low, nil), ENCARG(low)) ENCARG(cons_app'(if_low, nil)) -> c18(APP'(if_low, nil), ENCARG(if_low)) ENCARG(cons_app'(high, nil)) -> c18(APP'(high, nil), ENCARG(high)) ENCARG(cons_app'(if_high, nil)) -> c18(APP'(if_high, nil), ENCARG(if_high)) ENCARG(cons_app'(quicksort, nil)) -> c18(APP'(quicksort, nil), ENCARG(quicksort)) ENCARG(cons_app'(map, nil)) -> c18(APP'(map, nil), ENCARG(map)) ENCARG(cons_app'(filter, nil)) -> c18(APP'(filter, nil), ENCARG(filter)) ENCARG(cons_app'(filter2, nil)) -> c18(APP'(filter2, nil), ENCARG(filter2)) ENCARG(cons_app'(cons_app'(z0, z1), nil)) -> c18(APP'(app'(encArg(z0), encArg(z1)), nil), ENCARG(cons_app'(z0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(minus, nil)) -> c18(APP'(minus, nil), ENCARG(minus)) ENCARG(cons_app'(0, nil)) -> c18(APP'(0, nil), ENCARG(0)) ENCARG(cons_app'(s, nil)) -> c18(APP'(s, nil), ENCARG(s)) ENCARG(cons_app'(quot, nil)) -> c18(APP'(quot, nil), ENCARG(quot)) ENCARG(cons_app'(le, nil)) -> c18(APP'(le, nil), ENCARG(le)) ENCARG(cons_app'(true, nil)) -> c18(APP'(true, nil), ENCARG(true)) ENCARG(cons_app'(false, nil)) -> c18(APP'(false, nil), ENCARG(false)) ENCARG(cons_app'(app, nil)) -> c18(APP'(app, nil), ENCARG(app)) ENCARG(cons_app'(nil, nil)) -> c18(APP'(nil, nil), ENCARG(nil)) ENCARG(cons_app'(add, nil)) -> c18(APP'(add, nil), ENCARG(add)) ENCARG(cons_app'(low, nil)) -> c18(APP'(low, nil), ENCARG(low)) ENCARG(cons_app'(if_low, nil)) -> c18(APP'(if_low, nil), ENCARG(if_low)) ENCARG(cons_app'(high, nil)) -> c18(APP'(high, nil), ENCARG(high)) ENCARG(cons_app'(if_high, nil)) -> c18(APP'(if_high, nil), ENCARG(if_high)) ENCARG(cons_app'(quicksort, nil)) -> c18(APP'(quicksort, nil), ENCARG(quicksort)) ENCARG(cons_app'(map, nil)) -> c18(APP'(map, nil), ENCARG(map)) ENCARG(cons_app'(filter, nil)) -> c18(APP'(filter, nil), ENCARG(filter)) ENCARG(cons_app'(filter2, nil)) -> c18(APP'(filter2, nil), ENCARG(filter2)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing nodes: ENCARG(cons_app'(false, nil)) -> c18(APP'(false, nil), ENCARG(false)) ENCARG(cons_app'(if_high, nil)) -> c18(APP'(if_high, nil), ENCARG(if_high)) ENCARG(cons_app'(if_low, nil)) -> c18(APP'(if_low, nil), ENCARG(if_low)) ENCARG(cons_app'(map, nil)) -> c18(APP'(map, nil), ENCARG(map)) ENCARG(cons_app'(filter2, nil)) -> c18(APP'(filter2, nil), ENCARG(filter2)) ENCARG(cons_app'(filter, nil)) -> c18(APP'(filter, nil), ENCARG(filter)) ENCARG(cons_app'(low, nil)) -> c18(APP'(low, nil), ENCARG(low)) ENCARG(cons_app'(app, nil)) -> c18(APP'(app, nil), ENCARG(app)) ENCARG(cons_app'(le, nil)) -> c18(APP'(le, nil), ENCARG(le)) ENCARG(cons_app'(quot, nil)) -> c18(APP'(quot, nil), ENCARG(quot)) ENCARG(cons_app'(0, nil)) -> c18(APP'(0, nil), ENCARG(0)) ENCARG(cons_app'(s, nil)) -> c18(APP'(s, nil), ENCARG(s)) ENCARG(cons_app'(add, nil)) -> c18(APP'(add, nil), ENCARG(add)) ENCARG(cons_app'(high, nil)) -> c18(APP'(high, nil), ENCARG(high)) ENCARG(cons_app'(nil, nil)) -> c18(APP'(nil, nil), ENCARG(nil)) ENCARG(cons_app'(true, nil)) -> c18(APP'(true, nil), ENCARG(true)) ENCARG(cons_app'(minus, nil)) -> c18(APP'(minus, nil), ENCARG(minus)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(quicksort, nil)) -> c18(APP'(quicksort, nil), ENCARG(quicksort)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(quot) -> quot encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(app) -> app encArg(nil) -> nil encArg(add) -> add encArg(low) -> low encArg(if_low) -> if_low encArg(high) -> high encArg(if_high) -> if_high encArg(quicksort) -> quicksort encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app'(z0, z1)) -> app'(encArg(z0), encArg(z1)) app'(app'(minus, z0), 0) -> z0 app'(app'(minus, app'(s, z0)), app'(s, z1)) -> app'(app'(minus, z0), z1) app'(app'(quot, 0), app'(s, z0)) -> 0 app'(app'(quot, app'(s, z0)), app'(s, z1)) -> app'(s, app'(app'(quot, app'(app'(minus, z0), z1)), app'(s, z1))) app'(app'(le, 0), z0) -> true app'(app'(le, app'(s, z0)), 0) -> false app'(app'(le, app'(s, z0)), app'(s, z1)) -> app'(app'(le, z0), z1) app'(app'(app, nil), z0) -> z0 app'(app'(app, app'(app'(add, z0), z1)), z2) -> app'(app'(add, z0), app'(app'(app, z1), z2)) app'(app'(low, z0), nil) -> nil app'(app'(low, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(low, z0), z2)) app'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> app'(app'(low, z0), z2) app'(app'(high, z0), nil) -> nil app'(app'(high, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)) app'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> app'(app'(high, z0), z2) app'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> app'(app'(add, z1), app'(app'(high, z0), z2)) app'(quicksort, nil) -> nil app'(quicksort, app'(app'(add, z0), z1)) -> app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1)))) app'(app'(map, z0), nil) -> nil app'(app'(map, z0), app'(app'(add, z1), z2)) -> app'(app'(add, app'(z0, z1)), app'(app'(map, z0), z2)) app'(app'(filter, z0), nil) -> nil app'(app'(filter, z0), app'(app'(add, z1), z2)) -> app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2) app'(app'(app'(app'(filter2, true), z0), z1), z2) -> app'(app'(add, z1), app'(app'(filter, z0), z2)) app'(app'(app'(app'(filter2, false), z0), z1), z2) -> app'(app'(filter, z0), z2) Tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) ENCARG(cons_app'(x0, add)) -> c18(APP'(encArg(x0), add), ENCARG(x0)) ENCARG(cons_app'(x0, low)) -> c18(APP'(encArg(x0), low), ENCARG(x0)) ENCARG(cons_app'(x0, if_low)) -> c18(APP'(encArg(x0), if_low), ENCARG(x0)) ENCARG(cons_app'(x0, high)) -> c18(APP'(encArg(x0), high), ENCARG(x0)) ENCARG(cons_app'(x0, if_high)) -> c18(APP'(encArg(x0), if_high), ENCARG(x0)) ENCARG(cons_app'(x0, quicksort)) -> c18(APP'(encArg(x0), quicksort), ENCARG(x0)) ENCARG(cons_app'(x0, map)) -> c18(APP'(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app'(x0, filter)) -> c18(APP'(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app'(x0, filter2)) -> c18(APP'(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app'(minus, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(0, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(s, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quot, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(le, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(true, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(false, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(app, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(nil, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(add, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_low, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(if_high, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(quicksort, x1)) -> c18(APP'(quicksort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app'(map, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter, x1)) -> c18(ENCARG(x1)) ENCARG(cons_app'(filter2, x1)) -> c18(ENCARG(x1)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, true), z0), z1), z2)) ENCODE_APP'(x0, minus) -> c(APP'(encArg(x0), minus)) ENCODE_APP'(x0, 0) -> c(APP'(encArg(x0), 0)) ENCODE_APP'(x0, s) -> c(APP'(encArg(x0), s)) ENCODE_APP'(x0, quot) -> c(APP'(encArg(x0), quot)) ENCODE_APP'(x0, le) -> c(APP'(encArg(x0), le)) ENCODE_APP'(x0, true) -> c(APP'(encArg(x0), true)) ENCODE_APP'(x0, false) -> c(APP'(encArg(x0), false)) ENCODE_APP'(x0, app) -> c(APP'(encArg(x0), app)) ENCODE_APP'(x0, nil) -> c(APP'(encArg(x0), nil)) ENCODE_APP'(x0, add) -> c(APP'(encArg(x0), add)) ENCODE_APP'(x0, low) -> c(APP'(encArg(x0), low)) ENCODE_APP'(x0, if_low) -> c(APP'(encArg(x0), if_low)) ENCODE_APP'(x0, high) -> c(APP'(encArg(x0), high)) ENCODE_APP'(x0, if_high) -> c(APP'(encArg(x0), if_high)) ENCODE_APP'(x0, quicksort) -> c(APP'(encArg(x0), quicksort)) 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'(quicksort, x1) -> c(APP'(quicksort, encArg(x1))) ENCODE_APP'(cons_app'(z0, z1), x1) -> c(APP'(app'(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app'(x0, cons_app'(x1, minus))) -> c18(APP'(encArg(x0), app'(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app'(x1, minus))) ENCARG(cons_app'(x0, cons_app'(x1, 0))) -> c18(APP'(encArg(x0), app'(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app'(x1, 0))) ENCARG(cons_app'(x0, cons_app'(x1, s))) -> c18(APP'(encArg(x0), app'(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app'(x1, s))) ENCARG(cons_app'(x0, cons_app'(x1, quot))) -> c18(APP'(encArg(x0), app'(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app'(x1, quot))) ENCARG(cons_app'(x0, cons_app'(x1, le))) -> c18(APP'(encArg(x0), app'(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app'(x1, le))) ENCARG(cons_app'(x0, cons_app'(x1, true))) -> c18(APP'(encArg(x0), app'(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app'(x1, true))) ENCARG(cons_app'(x0, cons_app'(x1, false))) -> c18(APP'(encArg(x0), app'(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app'(x1, false))) ENCARG(cons_app'(x0, cons_app'(x1, app))) -> c18(APP'(encArg(x0), app'(encArg(x1), app)), ENCARG(x0), ENCARG(cons_app'(x1, app))) ENCARG(cons_app'(x0, cons_app'(x1, nil))) -> c18(APP'(encArg(x0), app'(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app'(x1, nil))) ENCARG(cons_app'(x0, cons_app'(x1, add))) -> c18(APP'(encArg(x0), app'(encArg(x1), add)), ENCARG(x0), ENCARG(cons_app'(x1, add))) ENCARG(cons_app'(x0, cons_app'(x1, low))) -> c18(APP'(encArg(x0), app'(encArg(x1), low)), ENCARG(x0), ENCARG(cons_app'(x1, low))) ENCARG(cons_app'(x0, cons_app'(x1, if_low))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_low)), ENCARG(x0), ENCARG(cons_app'(x1, if_low))) ENCARG(cons_app'(x0, cons_app'(x1, high))) -> c18(APP'(encArg(x0), app'(encArg(x1), high)), ENCARG(x0), ENCARG(cons_app'(x1, high))) ENCARG(cons_app'(x0, cons_app'(x1, if_high))) -> c18(APP'(encArg(x0), app'(encArg(x1), if_high)), ENCARG(x0), ENCARG(cons_app'(x1, if_high))) ENCARG(cons_app'(x0, cons_app'(x1, quicksort))) -> c18(APP'(encArg(x0), app'(encArg(x1), quicksort)), ENCARG(x0), ENCARG(cons_app'(x1, quicksort))) ENCARG(cons_app'(x0, cons_app'(x1, map))) -> c18(APP'(encArg(x0), app'(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app'(x1, map))) ENCARG(cons_app'(x0, cons_app'(x1, filter))) -> c18(APP'(encArg(x0), app'(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app'(x1, filter))) ENCARG(cons_app'(x0, cons_app'(x1, filter2))) -> c18(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)))) -> c18(APP'(encArg(x0), app'(encArg(x1), app'(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app'(x1, cons_app'(z0, z1)))) ENCARG(cons_app'(x0, cons_app'(minus, x2))) -> c18(APP'(encArg(x0), app'(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(minus, x2))) ENCARG(cons_app'(x0, cons_app'(0, x2))) -> c18(APP'(encArg(x0), app'(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(0, x2))) ENCARG(cons_app'(x0, cons_app'(s, x2))) -> c18(APP'(encArg(x0), app'(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(s, x2))) ENCARG(cons_app'(x0, cons_app'(quot, x2))) -> c18(APP'(encArg(x0), app'(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quot, x2))) ENCARG(cons_app'(x0, cons_app'(le, x2))) -> c18(APP'(encArg(x0), app'(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(le, x2))) ENCARG(cons_app'(x0, cons_app'(true, x2))) -> c18(APP'(encArg(x0), app'(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(true, x2))) ENCARG(cons_app'(x0, cons_app'(false, x2))) -> c18(APP'(encArg(x0), app'(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(false, x2))) ENCARG(cons_app'(x0, cons_app'(app, x2))) -> c18(APP'(encArg(x0), app'(app, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(app, x2))) ENCARG(cons_app'(x0, cons_app'(nil, x2))) -> c18(APP'(encArg(x0), app'(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(nil, x2))) ENCARG(cons_app'(x0, cons_app'(add, x2))) -> c18(APP'(encArg(x0), app'(add, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(add, x2))) ENCARG(cons_app'(x0, cons_app'(low, x2))) -> c18(APP'(encArg(x0), app'(low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(low, x2))) ENCARG(cons_app'(x0, cons_app'(if_low, x2))) -> c18(APP'(encArg(x0), app'(if_low, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_low, x2))) ENCARG(cons_app'(x0, cons_app'(high, x2))) -> c18(APP'(encArg(x0), app'(high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(high, x2))) ENCARG(cons_app'(x0, cons_app'(if_high, x2))) -> c18(APP'(encArg(x0), app'(if_high, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(if_high, x2))) ENCARG(cons_app'(x0, cons_app'(quicksort, x2))) -> c18(APP'(encArg(x0), app'(quicksort, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(quicksort, x2))) ENCARG(cons_app'(x0, cons_app'(map, x2))) -> c18(APP'(encArg(x0), app'(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(map, x2))) ENCARG(cons_app'(x0, cons_app'(filter, x2))) -> c18(APP'(encArg(x0), app'(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app'(filter, x2))) ENCARG(cons_app'(x0, cons_app'(filter2, x2))) -> c18(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))) -> c18(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))) -> c18(APP'(app'(encArg(z0), encArg(z1)), app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(z0, z1)), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(minus, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(0, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(s, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quot, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(le, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(true, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(false, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(app, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(nil, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(add, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_low, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(if_high, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(quicksort, cons_app'(x1, x2))) -> c18(APP'(quicksort, app'(encArg(x1), encArg(x2))), ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(map, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(filter2, cons_app'(x1, x2))) -> c18(ENCARG(cons_app'(x1, x2))) ENCARG(cons_app'(cons_app'(x0, minus), x2)) -> c18(APP'(app'(encArg(x0), minus), encArg(x2)), ENCARG(cons_app'(x0, minus)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, 0), x2)) -> c18(APP'(app'(encArg(x0), 0), encArg(x2)), ENCARG(cons_app'(x0, 0)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, s), x2)) -> c18(APP'(app'(encArg(x0), s), encArg(x2)), ENCARG(cons_app'(x0, s)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quot), x2)) -> c18(APP'(app'(encArg(x0), quot), encArg(x2)), ENCARG(cons_app'(x0, quot)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, le), x2)) -> c18(APP'(app'(encArg(x0), le), encArg(x2)), ENCARG(cons_app'(x0, le)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, true), x2)) -> c18(APP'(app'(encArg(x0), true), encArg(x2)), ENCARG(cons_app'(x0, true)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, false), x2)) -> c18(APP'(app'(encArg(x0), false), encArg(x2)), ENCARG(cons_app'(x0, false)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, app), x2)) -> c18(APP'(app'(encArg(x0), app), encArg(x2)), ENCARG(cons_app'(x0, app)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, nil), x2)) -> c18(APP'(app'(encArg(x0), nil), encArg(x2)), ENCARG(cons_app'(x0, nil)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, add), x2)) -> c18(APP'(app'(encArg(x0), add), encArg(x2)), ENCARG(cons_app'(x0, add)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, low), x2)) -> c18(APP'(app'(encArg(x0), low), encArg(x2)), ENCARG(cons_app'(x0, low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_low), x2)) -> c18(APP'(app'(encArg(x0), if_low), encArg(x2)), ENCARG(cons_app'(x0, if_low)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, high), x2)) -> c18(APP'(app'(encArg(x0), high), encArg(x2)), ENCARG(cons_app'(x0, high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, if_high), x2)) -> c18(APP'(app'(encArg(x0), if_high), encArg(x2)), ENCARG(cons_app'(x0, if_high)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, quicksort), x2)) -> c18(APP'(app'(encArg(x0), quicksort), encArg(x2)), ENCARG(cons_app'(x0, quicksort)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, map), x2)) -> c18(APP'(app'(encArg(x0), map), encArg(x2)), ENCARG(cons_app'(x0, map)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter), x2)) -> c18(APP'(app'(encArg(x0), filter), encArg(x2)), ENCARG(cons_app'(x0, filter)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, filter2), x2)) -> c18(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)) -> c18(APP'(app'(encArg(x0), app'(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app'(x0, cons_app'(z0, z1))), ENCARG(x2)) ENCARG(cons_app'(cons_app'(minus, x1), x2)) -> c18(APP'(app'(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app'(minus, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quot, x1), x2)) -> c18(APP'(app'(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quot, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(le, x1), x2)) -> c18(APP'(app'(le, encArg(x1)), encArg(x2)), ENCARG(cons_app'(le, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(app, x1), x2)) -> c18(APP'(app'(app, encArg(x1)), encArg(x2)), ENCARG(cons_app'(app, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(low, x1), x2)) -> c18(APP'(app'(low, encArg(x1)), encArg(x2)), ENCARG(cons_app'(low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(high, x1), x2)) -> c18(APP'(app'(high, encArg(x1)), encArg(x2)), ENCARG(cons_app'(high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(quicksort, x1), x2)) -> c18(APP'(app'(quicksort, encArg(x1)), encArg(x2)), ENCARG(cons_app'(quicksort, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(map, x1), x2)) -> c18(APP'(app'(map, encArg(x1)), encArg(x2)), ENCARG(cons_app'(map, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter, x1), x2)) -> c18(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)) -> c18(APP'(app'(app'(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app'(cons_app'(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(x0, x1), minus)) -> c18(APP'(app'(encArg(x0), encArg(x1)), minus), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), 0)) -> c18(APP'(app'(encArg(x0), encArg(x1)), 0), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), s)) -> c18(APP'(app'(encArg(x0), encArg(x1)), s), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quot)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quot), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), le)) -> c18(APP'(app'(encArg(x0), encArg(x1)), le), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), true)) -> c18(APP'(app'(encArg(x0), encArg(x1)), true), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), false)) -> c18(APP'(app'(encArg(x0), encArg(x1)), false), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), app)) -> c18(APP'(app'(encArg(x0), encArg(x1)), app), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), nil)) -> c18(APP'(app'(encArg(x0), encArg(x1)), nil), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), add)) -> c18(APP'(app'(encArg(x0), encArg(x1)), add), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_low)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_low), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), if_high)) -> c18(APP'(app'(encArg(x0), encArg(x1)), if_high), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), quicksort)) -> c18(APP'(app'(encArg(x0), encArg(x1)), quicksort), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), map)) -> c18(APP'(app'(encArg(x0), encArg(x1)), map), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(x0, x1), filter2)) -> c18(APP'(app'(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app'(x0, x1))) ENCARG(cons_app'(cons_app'(0, x1), x2)) -> c18(ENCARG(cons_app'(0, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(s, x1), x2)) -> c18(ENCARG(cons_app'(s, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(true, x1), x2)) -> c18(ENCARG(cons_app'(true, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(false, x1), x2)) -> c18(ENCARG(cons_app'(false, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(nil, x1), x2)) -> c18(ENCARG(cons_app'(nil, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(add, x1), x2)) -> c18(ENCARG(cons_app'(add, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_low, x1), x2)) -> c18(ENCARG(cons_app'(if_low, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(if_high, x1), x2)) -> c18(ENCARG(cons_app'(if_high, x1)), ENCARG(x2)) ENCARG(cons_app'(cons_app'(filter2, x1), x2)) -> c18(ENCARG(cons_app'(filter2, x1)), ENCARG(x2)) ENCARG(cons_app'(quicksort, nil)) -> c18(APP'(quicksort, nil)) S tuples: APP'(app'(minus, z0), 0) -> c38 APP'(app'(quot, 0), app'(s, z0)) -> c40 APP'(app'(le, 0), z0) -> c42 APP'(app'(le, app'(s, z0)), 0) -> c43 APP'(app'(app, nil), z0) -> c45 APP'(app'(low, z0), nil) -> c47 APP'(app'(high, z0), nil) -> c51 APP'(quicksort, nil) -> c55 APP'(app'(map, z0), nil) -> c57 APP'(app'(filter, z0), nil) -> c59 APP'(app'(minus, app'(s, z0)), app'(s, z1)) -> c39(APP'(app'(minus, z0), z1)) APP'(app'(le, app'(s, z0)), app'(s, z1)) -> c44(APP'(app'(le, z0), z1)) APP'(app'(app, app'(app'(add, z0), z1)), z2) -> c46(APP'(app'(app, z1), z2)) APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2)) -> c49(APP'(app'(low, z0), z2)) APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2)) -> c50(APP'(app'(low, z0), z2)) APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2)) -> c53(APP'(app'(high, z0), z2)) APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2)) -> c54(APP'(app'(high, z0), z2)) APP'(app'(map, z0), app'(app'(add, z1), z2)) -> c58(APP'(z0, z1), APP'(app'(map, z0), z2)) APP'(app'(app'(app'(filter2, true), z0), z1), z2) -> c61(APP'(app'(filter, z0), z2)) APP'(app'(app'(app'(filter2, false), z0), z1), z2) -> c62(APP'(app'(filter, z0), z2)) APP'(app'(quot, app'(s, z0)), app'(s, 0)) -> c41(APP'(app'(quot, z0), app'(s, 0)), APP'(app'(minus, z0), 0)) APP'(app'(quot, app'(s, app'(s, z0))), app'(s, app'(s, z1))) -> c41(APP'(app'(quot, app'(app'(minus, z0), z1)), app'(s, app'(s, z1))), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(low, z0), app'(app'(add, 0), x2)) -> c48(APP'(app'(app'(if_low, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(low, 0), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(low, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c48(APP'(app'(app'(if_low, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(high, z0), app'(app'(add, 0), x2)) -> c52(APP'(app'(app'(if_high, true), z0), app'(app'(add, 0), x2)), APP'(app'(le, 0), z0)) APP'(app'(high, 0), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, false), 0), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), 0)) APP'(app'(high, app'(s, z1)), app'(app'(add, app'(s, z0)), x2)) -> c52(APP'(app'(app'(if_high, app'(app'(le, z0), z1)), app'(s, z1)), app'(app'(add, app'(s, z0)), x2)), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), nil))), app'(app'(add, z0), app'(quicksort, nil))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(quicksort, app'(app'(add, z0), nil)) -> c56(APP'(app'(app, app'(quicksort, nil)), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), nil)))), APP'(quicksort, app'(app'(low, z0), nil)), APP'(app'(low, z0), nil), APP'(quicksort, app'(app'(high, z0), nil)), APP'(app'(high, z0), nil)) APP'(quicksort, app'(app'(add, z0), app'(app'(add, z1), z2))) -> c56(APP'(app'(app, app'(quicksort, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2)))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))))), APP'(quicksort, app'(app'(low, z0), app'(app'(add, z1), z2))), APP'(app'(low, z0), app'(app'(add, z1), z2)), APP'(quicksort, app'(app'(high, z0), app'(app'(add, z1), z2))), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(minus, z0)), app'(app'(add, 0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(minus, z0)), 0), x2), APP'(app'(minus, z0), 0)) APP'(app'(filter, app'(minus, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(minus, z0), z1)), app'(minus, app'(s, z0))), app'(s, z1)), x2), APP'(app'(minus, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(le, 0)), app'(app'(add, z0), x2)) -> c60(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'(add, 0), x2)) -> c60(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'(add, app'(s, z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(le, z0), z1)), app'(le, app'(s, z0))), app'(s, z1)), x2), APP'(app'(le, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, nil)), app'(app'(add, z0), x2)) -> c60(APP'(app'(app'(app'(filter2, z0), app'(app, nil)), z0), x2), APP'(app'(app, nil), z0)) APP'(app'(filter, app'(low, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_low, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(low, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(low, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_low, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(low, z0), z2)), app'(app'(if_low, false), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_low, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(if_high, app'(app'(le, z1), z0)), z0), app'(app'(add, z1), z2))), app'(high, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(high, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(if_high, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(high, z0), z2)), app'(app'(if_high, true), z0)), app'(app'(add, z1), z2)), x2), APP'(app'(app'(if_high, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, app'(app'(add, z0), z1)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app, app'(quicksort, app'(app'(low, z0), z1))), app'(app'(add, z0), app'(quicksort, app'(app'(high, z0), z1))))), quicksort), app'(app'(add, z0), z1)), x2), APP'(quicksort, app'(app'(add, z0), z1))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(app'(app'(filter2, app'(z0, z1)), z0), z1), z2)), app'(filter, z0)), app'(app'(add, z1), z2)), x2), APP'(app'(filter, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(app'(app'(filter2, false), z0), z1)), app'(app'(add, z2), x2)) -> c60(APP'(app'(app'(app'(filter2, app'(app'(filter, z0), z2)), app'(app'(app'(filter2, false), z0), z1)), z2), x2), APP'(app'(app'(app'(filter2, false), z0), z1), z2)) APP'(app'(filter, app'(quot, 0)), app'(app'(add, app'(s, z0)), x2)) -> c60(APP'(app'(quot, 0), app'(s, z0))) APP'(app'(filter, app'(quot, app'(s, z0))), app'(app'(add, app'(s, z1)), x2)) -> c60(APP'(app'(quot, app'(s, z0)), app'(s, z1))) APP'(app'(filter, app'(app, app'(app'(add, z0), z1))), app'(app'(add, z2), x2)) -> c60(APP'(app'(app, app'(app'(add, z0), z1)), z2)) APP'(app'(filter, app'(low, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(low, z0), nil)) APP'(app'(filter, app'(app'(if_low, true), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_low, true), z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(high, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(high, z0), nil)) APP'(app'(filter, app'(app'(if_high, false), z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(app'(if_high, false), z0), app'(app'(add, z1), z2))) APP'(app'(filter, quicksort), app'(app'(add, nil), x2)) -> c60(APP'(quicksort, nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(map, z0), nil)) APP'(app'(filter, app'(map, z0)), app'(app'(add, app'(app'(add, z1), z2)), x2)) -> c60(APP'(app'(map, z0), app'(app'(add, z1), z2))) APP'(app'(filter, app'(filter, z0)), app'(app'(add, nil), x2)) -> c60(APP'(app'(filter, z0), nil)) APP'(app'(filter, app'(app'(app'(filter2, true), z0), z1)), app'(app'(add, z2), x2)) -> c60(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: c38, c40, c42, c43, c45, c47, c51, c55, c57, c59, c39_1, c44_1, c46_1, c49_1, c50_1, c53_1, c54_1, c58_2, c61_1, c62_1, c18_2, c18_1, c41_2, c48_2, c52_2, c56_5, c60_2, c60_1, c_1, c18_3