KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 251 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), 4 ms] (12) typed CpxTrs (13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (14) CpxTRS (15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (16) CpxRelTRS (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 34.5 s] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 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), 17 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (54) CdtProblem (55) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 174 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 34 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 313 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 184 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 18 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 16 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 88 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (154) 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(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, app(app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false ---------------------------------------- (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(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, app(app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, app(app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, app(app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(D, t) -> 1' app(D, constant) -> 0' app(D, app(app(+', x), y)) -> app(app(+', app(D, x)), app(D, y)) app(D, app(app(*', x), y)) -> app(app(+', app(app(*', y), app(D, x))), app(app(*', x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*', x), app(D, y))), app(app(pow, y), 2'))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+', app(app(*', app(app(*', y), app(app(pow, x), app(app(-, y), 1')))), app(D, x))), app(app(*', app(app(*', app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(D) -> D encArg(t) -> t encArg(1') -> 1' encArg(constant) -> constant encArg(0') -> 0' encArg(+') -> +' encArg(*') -> *' encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2') -> 2' encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1' encode_constant -> constant encode_0 -> 0' encode_+ -> +' encode_* -> *' encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2' encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: app(D, t) -> 1' app(D, constant) -> 0' app(D, app(app(+', x), y)) -> app(app(+', app(D, x)), app(D, y)) app(D, app(app(*', x), y)) -> app(app(+', app(app(*', y), app(D, x))), app(app(*', x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*', x), app(D, y))), app(app(pow, y), 2'))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+', app(app(*', app(app(*', y), app(app(pow, x), app(app(-, y), 1')))), app(D, x))), app(app(*', app(app(*', app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(D) -> D encArg(t) -> t encArg(1') -> 1' encArg(constant) -> constant encArg(0') -> 0' encArg(+') -> +' encArg(*') -> *' encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2') -> 2' encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1' encode_constant -> constant encode_0 -> 0' encode_+ -> +' encode_* -> *' encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2' encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Types: app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app D :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app t :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 1' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app constant :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 0' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app +' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app *' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app - :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app minus :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app div :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app pow :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 2' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app ln :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app map :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app nil :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app cons :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app filter :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app filter2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app true :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app false :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encArg :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app cons_app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_D :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_t :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_1 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_constant :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_0 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_+ :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_* :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_- :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_minus :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_div :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_pow :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_ln :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_map :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_nil :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_cons :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_filter :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_filter2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_true :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_false :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app hole_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app gen_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false: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(D, t) -> 1' app(D, constant) -> 0' app(D, app(app(+', x), y)) -> app(app(+', app(D, x)), app(D, y)) app(D, app(app(*', x), y)) -> app(app(+', app(app(*', y), app(D, x))), app(app(*', x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*', x), app(D, y))), app(app(pow, y), 2'))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+', app(app(*', app(app(*', y), app(app(pow, x), app(app(-, y), 1')))), app(D, x))), app(app(*', app(app(*', app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(D) -> D encArg(t) -> t encArg(1') -> 1' encArg(constant) -> constant encArg(0') -> 0' encArg(+') -> +' encArg(*') -> *' encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2') -> 2' encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1' encode_constant -> constant encode_0 -> 0' encode_+ -> +' encode_* -> *' encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2' encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Types: app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app D :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app t :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 1' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app constant :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 0' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app +' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app *' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app - :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app minus :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app div :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app pow :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app 2' :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app ln :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app map :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app nil :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app cons :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app filter :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app filter2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app true :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app false :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encArg :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app cons_app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_app :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_D :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_t :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_1 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_constant :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_0 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_+ :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_* :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_- :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_minus :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_div :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_pow :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_ln :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_map :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_nil :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_cons :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_filter :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_filter2 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_true :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app encode_false :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app hole_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app gen_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app Generator Equations: gen_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app2_3(0) <=> D gen_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app2_3(+(x, 1)) <=> cons_app(D, gen_D:t:1':constant:0':+':*':-:minus:div:pow:2':ln:map:nil:cons:filter:filter2:true:false:cons_app2_3(x)) The following defined symbols remain to be analysed: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, app(app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, app(app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, app(minus, x)) -> app(minus, app(D, x)) app(D, app(app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) app(D, app(ln, x)) -> app(app(div, app(D, x)), x) app(D, app(app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(D, t) -> 1 app(D, constant) -> 0 app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) app(D, c_app(ln, x)) -> app(app(div, app(D, x)), x) app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) app(c_app(map, f), nil) -> nil app(c_app(filter, f), nil) -> nil app(D, c_app(minus, x)) -> app(minus, app(D, x)) app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) The (relative) TRS S consists of the following rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(D, t) -> 1 [1] app(D, constant) -> 0 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) [1] app(D, c_app(ln, x)) -> app(app(div, app(D, x)), x) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(D, c_app(minus, x)) -> app(minus, app(D, x)) [1] app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) [1] encArg(D) -> D [0] encArg(t) -> t [0] encArg(1) -> 1 [0] encArg(constant) -> constant [0] encArg(0) -> 0 [0] encArg(+) -> + [0] encArg(*) -> * [0] encArg(-) -> - [0] encArg(minus) -> minus [0] encArg(div) -> div [0] encArg(pow) -> pow [0] encArg(2) -> 2 [0] encArg(ln) -> ln [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_D -> D [0] encode_t -> t [0] encode_1 -> 1 [0] encode_constant -> constant [0] encode_0 -> 0 [0] encode_+ -> + [0] encode_* -> * [0] encode_- -> - [0] encode_minus -> minus [0] encode_div -> div [0] encode_pow -> pow [0] encode_2 -> 2 [0] encode_ln -> ln [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [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(D, t) -> 1 [1] app(D, constant) -> 0 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) [1] app(D, c_app(ln, x)) -> app(app(div, app(D, x)), x) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(D, c_app(minus, x)) -> app(minus, app(D, x)) [1] app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) [1] encArg(D) -> D [0] encArg(t) -> t [0] encArg(1) -> 1 [0] encArg(constant) -> constant [0] encArg(0) -> 0 [0] encArg(+) -> + [0] encArg(*) -> * [0] encArg(-) -> - [0] encArg(minus) -> minus [0] encArg(div) -> div [0] encArg(pow) -> pow [0] encArg(2) -> 2 [0] encArg(ln) -> ln [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_D -> D [0] encode_t -> t [0] encode_1 -> 1 [0] encode_constant -> constant [0] encode_0 -> 0 [0] encode_+ -> + [0] encode_* -> * [0] encode_- -> - [0] encode_minus -> minus [0] encode_div -> div [0] encode_pow -> pow [0] encode_2 -> 2 [0] encode_ln -> ln [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] The TRS has the following type information: app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app 1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app 0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app c_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app * :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app + :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app - :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app 2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app cons_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_app_2 encode_D encode_t encode_1 encode_constant encode_0 encode_+ encode_* encode_- encode_minus encode_div encode_pow encode_2 encode_ln encode_map encode_nil encode_cons encode_filter encode_filter2 encode_true encode_false app_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_D -> null_encode_D [0] encode_t -> null_encode_t [0] encode_1 -> null_encode_1 [0] encode_constant -> null_encode_constant [0] encode_0 -> null_encode_0 [0] encode_+ -> null_encode_+ [0] encode_* -> null_encode_* [0] encode_- -> null_encode_- [0] encode_minus -> null_encode_minus [0] encode_div -> null_encode_div [0] encode_pow -> null_encode_pow [0] encode_2 -> null_encode_2 [0] encode_ln -> null_encode_ln [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_D, null_encode_t, null_encode_1, null_encode_constant, null_encode_0, null_encode_+, null_encode_*, null_encode_-, null_encode_minus, null_encode_div, null_encode_pow, null_encode_2, null_encode_ln, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(D, t) -> 1 [1] app(D, constant) -> 0 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) [1] app(D, c_app(ln, x)) -> app(app(div, app(D, x)), x) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(D, c_app(minus, x)) -> app(minus, app(D, x)) [1] app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) [1] encArg(D) -> D [0] encArg(t) -> t [0] encArg(1) -> 1 [0] encArg(constant) -> constant [0] encArg(0) -> 0 [0] encArg(+) -> + [0] encArg(*) -> * [0] encArg(-) -> - [0] encArg(minus) -> minus [0] encArg(div) -> div [0] encArg(pow) -> pow [0] encArg(2) -> 2 [0] encArg(ln) -> ln [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_D -> D [0] encode_t -> t [0] encode_1 -> 1 [0] encode_constant -> constant [0] encode_0 -> 0 [0] encode_+ -> + [0] encode_* -> * [0] encode_- -> - [0] encode_minus -> minus [0] encode_div -> div [0] encode_pow -> pow [0] encode_2 -> 2 [0] encode_ln -> ln [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_D -> null_encode_D [0] encode_t -> null_encode_t [0] encode_1 -> null_encode_1 [0] encode_constant -> null_encode_constant [0] encode_0 -> null_encode_0 [0] encode_+ -> null_encode_+ [0] encode_* -> null_encode_* [0] encode_- -> null_encode_- [0] encode_minus -> null_encode_minus [0] encode_div -> null_encode_div [0] encode_pow -> null_encode_pow [0] encode_2 -> null_encode_2 [0] encode_ln -> null_encode_ln [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app * :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app + :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app - :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(D, t) -> 1 [1] app(D, constant) -> 0 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) [1] app(D, c_app(ln, t)) -> app(app(div, 1), t) [2] app(D, c_app(ln, constant)) -> app(app(div, 0), constant) [2] app(D, c_app(ln, c_app(c_app(*, x333), y234))) -> app(app(div, app(app(+, app(app(*, y234), app(D, x333))), app(app(*, x333), app(D, y234)))), c_app(c_app(*, x333), y234)) [2] app(D, c_app(ln, c_app(ln, x334))) -> app(app(div, app(app(div, app(D, x334)), x334)), c_app(ln, x334)) [2] app(D, c_app(ln, c_app(minus, x335))) -> app(app(div, app(minus, app(D, x335))), c_app(minus, x335)) [2] app(D, c_app(ln, c_app(c_app(+, x336), y235))) -> app(app(div, app(app(+, app(D, x336)), app(D, y235))), c_app(c_app(+, x336), y235)) [2] app(D, c_app(ln, c_app(c_app(-, x337), y236))) -> app(app(div, app(app(-, app(D, x337)), app(D, y236))), c_app(c_app(-, x337), y236)) [2] app(D, c_app(ln, c_app(c_app(pow, x338), y237))) -> app(app(div, app(app(+, app(app(*, app(app(*, y237), app(app(pow, x338), app(app(-, y237), 1)))), app(D, x338))), app(app(*, app(app(*, app(app(pow, x338), y237)), app(ln, x338))), app(D, y237)))), c_app(c_app(pow, x338), y237)) [2] app(D, c_app(ln, c_app(c_app(div, x339), y238))) -> app(app(div, app(app(-, app(app(div, app(D, x339)), y238)), app(app(div, app(app(*, x339), app(D, y238))), app(app(pow, y238), 2)))), c_app(c_app(div, x339), y238)) [2] app(D, c_app(ln, x)) -> app(app(div, c_app(D, x)), x) [1] app(D, c_app(ln, x)) -> app(app(div, 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(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(D, c_app(minus, t)) -> app(minus, 1) [2] app(D, c_app(minus, constant)) -> app(minus, 0) [2] app(D, c_app(minus, c_app(c_app(*, x340), y239))) -> app(minus, app(app(+, app(app(*, y239), app(D, x340))), app(app(*, x340), app(D, y239)))) [2] app(D, c_app(minus, c_app(ln, x341))) -> app(minus, app(app(div, app(D, x341)), x341)) [2] app(D, c_app(minus, c_app(minus, x342))) -> app(minus, app(minus, app(D, x342))) [2] app(D, c_app(minus, c_app(c_app(+, x343), y240))) -> app(minus, app(app(+, app(D, x343)), app(D, y240))) [2] app(D, c_app(minus, c_app(c_app(-, x344), y241))) -> app(minus, app(app(-, app(D, x344)), app(D, y241))) [2] app(D, c_app(minus, c_app(c_app(pow, x345), y242))) -> app(minus, app(app(+, app(app(*, app(app(*, y242), app(app(pow, x345), app(app(-, y242), 1)))), app(D, x345))), app(app(*, app(app(*, app(app(pow, x345), y242)), app(ln, x345))), app(D, y242)))) [2] app(D, c_app(minus, c_app(c_app(div, x346), y243))) -> app(minus, app(app(-, app(app(div, app(D, x346)), y243)), app(app(div, app(app(*, x346), app(D, y243))), app(app(pow, y243), 2)))) [2] app(D, c_app(minus, x)) -> app(minus, c_app(D, x)) [1] app(D, c_app(minus, x)) -> app(minus, null_app) [1] app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(null_app, xs)) [1] app(c_app(filter, D), c_app(c_app(cons, t), xs)) -> app(app(app(app(filter2, 1), D), t), xs) [2] app(c_app(filter, D), c_app(c_app(cons, constant), xs)) -> app(app(app(app(filter2, 0), D), constant), xs) [2] app(c_app(filter, c_app(map, f5)), c_app(c_app(cons, c_app(c_app(cons, x3035), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(f5, x3035)), app(app(map, f5), xs1))), c_app(map, f5)), c_app(c_app(cons, x3035), xs1)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(c_app(*, x3036), y2164)), xs)) -> app(app(app(app(filter2, app(app(+, app(app(*, y2164), app(D, x3036))), app(app(*, x3036), app(D, y2164)))), D), c_app(c_app(*, x3036), y2164)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(ln, x3037)), xs)) -> app(app(app(app(filter2, app(app(div, app(D, x3037)), x3037)), D), c_app(ln, x3037)), xs) [2] app(c_app(filter, c_app(c_app(c_app(filter2, false), f6), x3038)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, f6), x)), c_app(c_app(c_app(filter2, false), f6), x3038)), x), xs) [2] app(c_app(filter, c_app(map, f7)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, f7)), nil), xs) [2] app(c_app(filter, c_app(filter, f8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, f8)), nil), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(minus, x3039)), xs)) -> app(app(app(app(filter2, app(minus, app(D, x3039))), D), c_app(minus, x3039)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(c_app(+, x3040), y2165)), xs)) -> app(app(app(app(filter2, app(app(+, app(D, x3040)), app(D, y2165))), D), c_app(c_app(+, x3040), y2165)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(c_app(-, x3041), y2166)), xs)) -> app(app(app(app(filter2, app(app(-, app(D, x3041)), app(D, y2166))), D), c_app(c_app(-, x3041), y2166)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(c_app(pow, x3042), y2167)), xs)) -> app(app(app(app(filter2, app(app(+, app(app(*, app(app(*, y2167), app(app(pow, x3042), app(app(-, y2167), 1)))), app(D, x3042))), app(app(*, app(app(*, app(app(pow, x3042), y2167)), app(ln, x3042))), app(D, y2167)))), D), c_app(c_app(pow, x3042), y2167)), xs) [2] app(c_app(filter, c_app(c_app(c_app(filter2, true), f9), x3043)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x3043), app(app(filter, f9), x))), c_app(c_app(c_app(filter2, true), f9), x3043)), x), xs) [2] app(c_app(filter, c_app(filter, f10)), c_app(c_app(cons, c_app(c_app(cons, x3044), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(f10, x3044)), f10), x3044), xs2)), c_app(filter, f10)), c_app(c_app(cons, x3044), xs2)), xs) [2] app(c_app(filter, D), c_app(c_app(cons, c_app(c_app(div, x3045), y2168)), xs)) -> app(app(app(app(filter2, app(app(-, app(app(div, app(D, x3045)), y2168)), app(app(div, app(app(*, x3045), app(D, y2168))), app(app(pow, y2168), 2)))), D), c_app(c_app(div, x3045), y2168)), xs) [2] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, c_app(f, x)), f), x), xs) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, null_app), f), x), xs) [1] app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) [1] encArg(D) -> D [0] encArg(t) -> t [0] encArg(1) -> 1 [0] encArg(constant) -> constant [0] encArg(0) -> 0 [0] encArg(+) -> + [0] encArg(*) -> * [0] encArg(-) -> - [0] encArg(minus) -> minus [0] encArg(div) -> div [0] encArg(pow) -> pow [0] encArg(2) -> 2 [0] encArg(ln) -> ln [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_D -> D [0] encode_t -> t [0] encode_1 -> 1 [0] encode_constant -> constant [0] encode_0 -> 0 [0] encode_+ -> + [0] encode_* -> * [0] encode_- -> - [0] encode_minus -> minus [0] encode_div -> div [0] encode_pow -> pow [0] encode_2 -> 2 [0] encode_ln -> ln [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_D -> null_encode_D [0] encode_t -> null_encode_t [0] encode_1 -> null_encode_1 [0] encode_constant -> null_encode_constant [0] encode_0 -> null_encode_0 [0] encode_+ -> null_encode_+ [0] encode_* -> null_encode_* [0] encode_- -> null_encode_- [0] encode_minus -> null_encode_minus [0] encode_div -> null_encode_div [0] encode_pow -> null_encode_pow [0] encode_2 -> null_encode_2 [0] encode_ln -> null_encode_ln [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app * :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app + :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app - :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: D => 6 t => 18 1 => 4 constant => 8 0 => 3 map => 14 cons => 7 * => 0 + => 1 ln => 13 div => 9 filter2 => 12 false => 10 filter => 11 nil => 16 minus => 15 - => 2 pow => 17 true => 19 2 => 5 null_encArg => 0 null_encode_app => 0 null_encode_D => 0 null_encode_t => 0 null_encode_1 => 0 null_encode_constant => 0 null_encode_0 => 0 null_encode_+ => 0 null_encode_* => 0 null_encode_- => 0 null_encode_minus => 0 null_encode_div => 0 null_encode_pow => 0 null_encode_2 => 0 null_encode_ln => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_encode_true => 0 null_encode_false => 0 null_app => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 2 }-> app(app(app(app(12, app(app(app(app(12, app(f10, x3044)), f10), x3044), xs2)), 1 + 11 + f10), 1 + (1 + 7 + x3044) + xs2), xs) :|: xs >= 0, xs2 >= 0, f10 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 7 + x3044) + xs2)) + xs, x3044 >= 0, z = 1 + 11 + (1 + 11 + f10) app(z, z') -{ 2 }-> app(app(app(app(12, app(app(9, app(6, x3037)), x3037)), 6), 1 + 13 + x3037), xs) :|: xs >= 0, z' = 1 + (1 + 7 + (1 + 13 + x3037)) + xs, z = 1 + 11 + 6, x3037 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(7, x3043), app(app(11, f9), x))), 1 + (1 + (1 + 12 + 19) + f9) + x3043), x), xs) :|: xs >= 0, x >= 0, x3043 >= 0, f9 >= 0, z = 1 + 11 + (1 + (1 + (1 + 12 + 19) + f9) + x3043), z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(7, app(f5, x3035)), app(app(14, f5), xs1))), 1 + 14 + f5), 1 + (1 + 7 + x3035) + xs1), xs) :|: z = 1 + 11 + (1 + 14 + f5), xs >= 0, x3035 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 7 + x3035) + xs1)) + xs, xs1 >= 0, f5 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(2, app(app(9, app(6, x3045)), y2168)), app(app(9, app(app(0, x3045), app(6, y2168))), app(app(17, y2168), 5)))), 6), 1 + (1 + 9 + x3045) + y2168), xs) :|: xs >= 0, z = 1 + 11 + 6, y2168 >= 0, x3045 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 9 + x3045) + y2168)) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(2, app(6, x3041)), app(6, y2166))), 6), 1 + (1 + 2 + x3041) + y2166), xs) :|: z' = 1 + (1 + 7 + (1 + (1 + 2 + x3041) + y2166)) + xs, y2166 >= 0, xs >= 0, z = 1 + 11 + 6, x3041 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(11, f6), x)), 1 + (1 + (1 + 12 + 10) + f6) + x3038), x), xs) :|: xs >= 0, x >= 0, f6 >= 0, x3038 >= 0, z = 1 + 11 + (1 + (1 + (1 + 12 + 10) + f6) + x3038), z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(app(0, y2164), app(6, x3036))), app(app(0, x3036), app(6, y2164)))), 6), 1 + (1 + 0 + x3036) + y2164), xs) :|: x3036 >= 0, xs >= 0, z' = 1 + (1 + 7 + (1 + (1 + 0 + x3036) + y2164)) + xs, z = 1 + 11 + 6, y2164 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(app(0, app(app(0, y2167), app(app(17, x3042), app(app(2, y2167), 4)))), app(6, x3042))), app(app(0, app(app(0, app(app(17, x3042), y2167)), app(13, x3042))), app(6, y2167)))), 6), 1 + (1 + 17 + x3042) + y2167), xs) :|: x3042 >= 0, xs >= 0, z' = 1 + (1 + 7 + (1 + (1 + 17 + x3042) + y2167)) + xs, z = 1 + 11 + 6, y2167 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(6, x3040)), app(6, y2165))), 6), 1 + (1 + 1 + x3040) + y2165), xs) :|: z' = 1 + (1 + 7 + (1 + (1 + 1 + x3040) + y2165)) + xs, xs >= 0, y2165 >= 0, z = 1 + 11 + 6, x3040 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(15, app(6, x3039))), 6), 1 + 15 + x3039), xs) :|: z' = 1 + (1 + 7 + (1 + 15 + x3039)) + xs, xs >= 0, x3039 >= 0, z = 1 + 11 + 6 app(z, z') -{ 2 }-> app(app(app(app(12, 4), 6), 18), xs) :|: xs >= 0, z = 1 + 11 + 6, z' = 1 + (1 + 7 + 18) + xs app(z, z') -{ 2 }-> app(app(app(app(12, 3), 6), 8), xs) :|: xs >= 0, z' = 1 + (1 + 7 + 8) + xs, z = 1 + 11 + 6 app(z, z') -{ 2 }-> app(app(app(app(12, 16), 1 + 14 + f7), 16), xs) :|: xs >= 0, z' = 1 + (1 + 7 + 16) + xs, f7 >= 0, z = 1 + 11 + (1 + 14 + f7) app(z, z') -{ 2 }-> app(app(app(app(12, 16), 1 + 11 + f8), 16), xs) :|: f8 >= 0, xs >= 0, z = 1 + 11 + (1 + 11 + f8), z' = 1 + (1 + 7 + 16) + xs app(z, z') -{ 1 }-> app(app(app(app(12, 0), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 11 + f, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(app(app(12, 1 + f + x), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 11 + f, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(9, app(app(9, app(6, x334)), x334)), 1 + 13 + x334) :|: z = 6, z' = 1 + 13 + (1 + 13 + x334), x334 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(2, app(app(9, app(6, x339)), y238)), app(app(9, app(app(0, x339), app(6, y238))), app(app(17, y238), 5)))), 1 + (1 + 9 + x339) + y238) :|: z' = 1 + 13 + (1 + (1 + 9 + x339) + y238), x339 >= 0, z = 6, y238 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(2, app(6, x337)), app(6, y236))), 1 + (1 + 2 + x337) + y236) :|: z' = 1 + 13 + (1 + (1 + 2 + x337) + y236), z = 6, y236 >= 0, x337 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(app(0, y234), app(6, x333))), app(app(0, x333), app(6, y234)))), 1 + (1 + 0 + x333) + y234) :|: z' = 1 + 13 + (1 + (1 + 0 + x333) + y234), x333 >= 0, z = 6, y234 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(app(0, app(app(0, y237), app(app(17, x338), app(app(2, y237), 4)))), app(6, x338))), app(app(0, app(app(0, app(app(17, x338), y237)), app(13, x338))), app(6, y237)))), 1 + (1 + 17 + x338) + y237) :|: z' = 1 + 13 + (1 + (1 + 17 + x338) + y237), z = 6, x338 >= 0, y237 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(6, x336)), app(6, y235))), 1 + (1 + 1 + x336) + y235) :|: y235 >= 0, z' = 1 + 13 + (1 + (1 + 1 + x336) + y235), z = 6, x336 >= 0 app(z, z') -{ 2 }-> app(app(9, app(15, app(6, x335))), 1 + 15 + x335) :|: z = 6, z' = 1 + 13 + (1 + 15 + x335), x335 >= 0 app(z, z') -{ 2 }-> app(app(9, 4), 18) :|: z' = 1 + 13 + 18, z = 6 app(z, z') -{ 2 }-> app(app(9, 3), 8) :|: z = 6, z' = 1 + 13 + 8 app(z, z') -{ 1 }-> app(app(9, 0), x) :|: x >= 0, z = 6, z' = 1 + 13 + x app(z, z') -{ 1 }-> app(app(9, 1 + 6 + x), x) :|: x >= 0, z = 6, z' = 1 + 13 + x app(z, z') -{ 1 }-> app(app(7, app(f, x)), app(app(14, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 14 + f, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(2, app(app(9, app(6, x)), y)), app(app(9, app(app(0, x), app(6, y))), app(app(17, y), 5))) :|: z' = 1 + (1 + 9 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(2, app(6, x)), app(6, y)) :|: x >= 0, y >= 0, z = 6, z' = 1 + (1 + 2 + x) + y app(z, z') -{ 1 }-> app(app(1, app(app(0, y), app(6, x))), app(app(0, x), app(6, y))) :|: z' = 1 + (1 + 0 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(app(0, app(app(0, y), app(app(17, x), app(app(2, y), 4)))), app(6, x))), app(app(0, app(app(0, app(app(17, x), y)), app(13, x))), app(6, y))) :|: z' = 1 + (1 + 17 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(6, x)), app(6, y)) :|: z' = 1 + (1 + 1 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 2 }-> app(15, app(app(9, app(6, x341)), x341)) :|: z = 6, x341 >= 0, z' = 1 + 15 + (1 + 13 + x341) app(z, z') -{ 2 }-> app(15, app(app(2, app(app(9, app(6, x346)), y243)), app(app(9, app(app(0, x346), app(6, y243))), app(app(17, y243), 5)))) :|: z' = 1 + 15 + (1 + (1 + 9 + x346) + y243), z = 6, y243 >= 0, x346 >= 0 app(z, z') -{ 2 }-> app(15, app(app(2, app(6, x344)), app(6, y241))) :|: z' = 1 + 15 + (1 + (1 + 2 + x344) + y241), z = 6, x344 >= 0, y241 >= 0 app(z, z') -{ 2 }-> app(15, app(app(1, app(app(0, y239), app(6, x340))), app(app(0, x340), app(6, y239)))) :|: y239 >= 0, z = 6, x340 >= 0, z' = 1 + 15 + (1 + (1 + 0 + x340) + y239) app(z, z') -{ 2 }-> app(15, app(app(1, app(app(0, app(app(0, y242), app(app(17, x345), app(app(2, y242), 4)))), app(6, x345))), app(app(0, app(app(0, app(app(17, x345), y242)), app(13, x345))), app(6, y242)))) :|: z' = 1 + 15 + (1 + (1 + 17 + x345) + y242), z = 6, x345 >= 0, y242 >= 0 app(z, z') -{ 2 }-> app(15, app(app(1, app(6, x343)), app(6, y240))) :|: x343 >= 0, z' = 1 + 15 + (1 + (1 + 1 + x343) + y240), z = 6, y240 >= 0 app(z, z') -{ 2 }-> app(15, app(15, app(6, x342))) :|: z' = 1 + 15 + (1 + 15 + x342), z = 6, x342 >= 0 app(z, z') -{ 2 }-> app(15, 4) :|: z = 6, z' = 1 + 15 + 18 app(z, z') -{ 2 }-> app(15, 3) :|: z = 6, z' = 1 + 15 + 8 app(z, z') -{ 1 }-> app(15, 0) :|: z' = 1 + 15 + x, x >= 0, z = 6 app(z, z') -{ 1 }-> app(15, 1 + 6 + x) :|: z' = 1 + 15 + x, x >= 0, z = 6 app(z, z') -{ 1 }-> app(0, xs) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 10) + f) + x app(z, z') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(0, app(1 + 11 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 7 + x, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 7 + x, app(1 + 11 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 11 + f, xs) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 10) + f) + x app(z, z') -{ 1 }-> 4 :|: z' = 18, z = 6 app(z, z') -{ 1 }-> 3 :|: z = 6, z' = 8 app(z, z') -{ 1 }-> 16 :|: f >= 0, z = 1 + 14 + f, z' = 16 app(z, z') -{ 1 }-> 16 :|: f >= 0, z = 1 + 11 + f, z' = 16 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 }-> 19 :|: z = 19 encArg(z) -{ 0 }-> 18 :|: z = 18 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 :|: encode_+ -{ 0 }-> 1 :|: encode_+ -{ 0 }-> 0 :|: encode_- -{ 0 }-> 2 :|: encode_- -{ 0 }-> 0 :|: encode_0 -{ 0 }-> 3 :|: encode_0 -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 4 :|: encode_1 -{ 0 }-> 0 :|: encode_2 -{ 0 }-> 5 :|: encode_2 -{ 0 }-> 0 :|: encode_D -{ 0 }-> 6 :|: encode_D -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 7 :|: encode_cons -{ 0 }-> 0 :|: encode_constant -{ 0 }-> 8 :|: encode_constant -{ 0 }-> 0 :|: encode_div -{ 0 }-> 9 :|: encode_div -{ 0 }-> 0 :|: encode_false -{ 0 }-> 10 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 11 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 12 :|: encode_filter2 -{ 0 }-> 0 :|: encode_ln -{ 0 }-> 13 :|: encode_ln -{ 0 }-> 0 :|: encode_map -{ 0 }-> 14 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 15 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 16 :|: encode_nil -{ 0 }-> 0 :|: encode_pow -{ 0 }-> 17 :|: encode_pow -{ 0 }-> 0 :|: encode_t -{ 0 }-> 18 :|: encode_t -{ 0 }-> 0 :|: encode_true -{ 0 }-> 19 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (27) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 2 }-> app(app(app(app(12, app(app(app(app(12, app(z - 24, x3044)), z - 24), x3044), xs2)), 1 + 11 + (z - 24)), 1 + (1 + 7 + x3044) + xs2), xs) :|: xs >= 0, xs2 >= 0, z - 24 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 7 + x3044) + xs2)) + xs, x3044 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(9, app(6, x3037)), x3037)), 6), 1 + 13 + x3037), xs) :|: xs >= 0, z' = 1 + (1 + 7 + (1 + 13 + x3037)) + xs, z = 1 + 11 + 6, x3037 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(7, x3043), app(app(11, f9), x))), 1 + (1 + (1 + 12 + 19) + f9) + x3043), x), xs) :|: xs >= 0, x >= 0, x3043 >= 0, f9 >= 0, z = 1 + 11 + (1 + (1 + (1 + 12 + 19) + f9) + x3043), z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(7, app(z - 27, x3035)), app(app(14, z - 27), xs1))), 1 + 14 + (z - 27)), 1 + (1 + 7 + x3035) + xs1), xs) :|: xs >= 0, x3035 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 7 + x3035) + xs1)) + xs, xs1 >= 0, z - 27 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(2, app(app(9, app(6, x3045)), y2168)), app(app(9, app(app(0, x3045), app(6, y2168))), app(app(17, y2168), 5)))), 6), 1 + (1 + 9 + x3045) + y2168), xs) :|: xs >= 0, z = 1 + 11 + 6, y2168 >= 0, x3045 >= 0, z' = 1 + (1 + 7 + (1 + (1 + 9 + x3045) + y2168)) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(2, app(6, x3041)), app(6, y2166))), 6), 1 + (1 + 2 + x3041) + y2166), xs) :|: z' = 1 + (1 + 7 + (1 + (1 + 2 + x3041) + y2166)) + xs, y2166 >= 0, xs >= 0, z = 1 + 11 + 6, x3041 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(11, f6), x)), 1 + (1 + (1 + 12 + 10) + f6) + x3038), x), xs) :|: xs >= 0, x >= 0, f6 >= 0, x3038 >= 0, z = 1 + 11 + (1 + (1 + (1 + 12 + 10) + f6) + x3038), z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(app(0, y2164), app(6, x3036))), app(app(0, x3036), app(6, y2164)))), 6), 1 + (1 + 0 + x3036) + y2164), xs) :|: x3036 >= 0, xs >= 0, z' = 1 + (1 + 7 + (1 + (1 + 0 + x3036) + y2164)) + xs, z = 1 + 11 + 6, y2164 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(app(0, app(app(0, y2167), app(app(17, x3042), app(app(2, y2167), 4)))), app(6, x3042))), app(app(0, app(app(0, app(app(17, x3042), y2167)), app(13, x3042))), app(6, y2167)))), 6), 1 + (1 + 17 + x3042) + y2167), xs) :|: x3042 >= 0, xs >= 0, z' = 1 + (1 + 7 + (1 + (1 + 17 + x3042) + y2167)) + xs, z = 1 + 11 + 6, y2167 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(app(1, app(6, x3040)), app(6, y2165))), 6), 1 + (1 + 1 + x3040) + y2165), xs) :|: z' = 1 + (1 + 7 + (1 + (1 + 1 + x3040) + y2165)) + xs, xs >= 0, y2165 >= 0, z = 1 + 11 + 6, x3040 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, app(15, app(6, x3039))), 6), 1 + 15 + x3039), xs) :|: z' = 1 + (1 + 7 + (1 + 15 + x3039)) + xs, xs >= 0, x3039 >= 0, z = 1 + 11 + 6 app(z, z') -{ 2 }-> app(app(app(app(12, 4), 6), 18), z' - 27) :|: z' - 27 >= 0, z = 1 + 11 + 6 app(z, z') -{ 2 }-> app(app(app(app(12, 3), 6), 8), z' - 17) :|: z' - 17 >= 0, z = 1 + 11 + 6 app(z, z') -{ 2 }-> app(app(app(app(12, 16), 1 + 14 + (z - 27)), 16), z' - 25) :|: z' - 25 >= 0, z - 27 >= 0 app(z, z') -{ 2 }-> app(app(app(app(12, 16), 1 + 11 + (z - 24)), 16), z' - 25) :|: z - 24 >= 0, z' - 25 >= 0 app(z, z') -{ 1 }-> app(app(app(app(12, 0), z - 12), x), xs) :|: z - 12 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(app(app(12, 1 + (z - 12) + x), z - 12), x), xs) :|: z - 12 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 2 }-> app(app(9, app(app(9, app(6, z' - 28)), z' - 28)), 1 + 13 + (z' - 28)) :|: z = 6, z' - 28 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(2, app(app(9, app(6, x339)), y238)), app(app(9, app(app(0, x339), app(6, y238))), app(app(17, y238), 5)))), 1 + (1 + 9 + x339) + y238) :|: z' = 1 + 13 + (1 + (1 + 9 + x339) + y238), x339 >= 0, z = 6, y238 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(2, app(6, x337)), app(6, y236))), 1 + (1 + 2 + x337) + y236) :|: z' = 1 + 13 + (1 + (1 + 2 + x337) + y236), z = 6, y236 >= 0, x337 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(app(0, y234), app(6, x333))), app(app(0, x333), app(6, y234)))), 1 + (1 + 0 + x333) + y234) :|: z' = 1 + 13 + (1 + (1 + 0 + x333) + y234), x333 >= 0, z = 6, y234 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(app(0, app(app(0, y237), app(app(17, x338), app(app(2, y237), 4)))), app(6, x338))), app(app(0, app(app(0, app(app(17, x338), y237)), app(13, x338))), app(6, y237)))), 1 + (1 + 17 + x338) + y237) :|: z' = 1 + 13 + (1 + (1 + 17 + x338) + y237), z = 6, x338 >= 0, y237 >= 0 app(z, z') -{ 2 }-> app(app(9, app(app(1, app(6, x336)), app(6, y235))), 1 + (1 + 1 + x336) + y235) :|: y235 >= 0, z' = 1 + 13 + (1 + (1 + 1 + x336) + y235), z = 6, x336 >= 0 app(z, z') -{ 2 }-> app(app(9, app(15, app(6, z' - 30))), 1 + 15 + (z' - 30)) :|: z = 6, z' - 30 >= 0 app(z, z') -{ 2 }-> app(app(9, 4), 18) :|: z' = 1 + 13 + 18, z = 6 app(z, z') -{ 2 }-> app(app(9, 3), 8) :|: z = 6, z' = 1 + 13 + 8 app(z, z') -{ 1 }-> app(app(9, 0), z' - 14) :|: z' - 14 >= 0, z = 6 app(z, z') -{ 1 }-> app(app(9, 1 + 6 + (z' - 14)), z' - 14) :|: z' - 14 >= 0, z = 6 app(z, z') -{ 1 }-> app(app(7, app(z - 15, x)), app(app(14, z - 15), xs)) :|: z - 15 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(2, app(app(9, app(6, x)), y)), app(app(9, app(app(0, x), app(6, y))), app(app(17, y), 5))) :|: z' = 1 + (1 + 9 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(2, app(6, x)), app(6, y)) :|: x >= 0, y >= 0, z = 6, z' = 1 + (1 + 2 + x) + y app(z, z') -{ 1 }-> app(app(1, app(app(0, y), app(6, x))), app(app(0, x), app(6, y))) :|: z' = 1 + (1 + 0 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(app(0, app(app(0, y), app(app(17, x), app(app(2, y), 4)))), app(6, x))), app(app(0, app(app(0, app(app(17, x), y)), app(13, x))), app(6, y))) :|: z' = 1 + (1 + 17 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(6, x)), app(6, y)) :|: z' = 1 + (1 + 1 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 2 }-> app(15, app(app(9, app(6, z' - 30)), z' - 30)) :|: z = 6, z' - 30 >= 0 app(z, z') -{ 2 }-> app(15, app(app(2, app(app(9, app(6, x346)), y243)), app(app(9, app(app(0, x346), app(6, y243))), app(app(17, y243), 5)))) :|: z' = 1 + 15 + (1 + (1 + 9 + x346) + y243), z = 6, y243 >= 0, x346 >= 0 app(z, z') -{ 2 }-> app(15, app(app(2, app(6, x344)), app(6, y241))) :|: z' = 1 + 15 + (1 + (1 + 2 + x344) + y241), z = 6, x344 >= 0, y241 >= 0 app(z, z') -{ 2 }-> app(15, app(app(1, app(app(0, y239), app(6, x340))), app(app(0, x340), app(6, y239)))) :|: y239 >= 0, z = 6, x340 >= 0, z' = 1 + 15 + (1 + (1 + 0 + x340) + y239) app(z, z') -{ 2 }-> app(15, app(app(1, app(app(0, app(app(0, y242), app(app(17, x345), app(app(2, y242), 4)))), app(6, x345))), app(app(0, app(app(0, app(app(17, x345), y242)), app(13, x345))), app(6, y242)))) :|: z' = 1 + 15 + (1 + (1 + 17 + x345) + y242), z = 6, x345 >= 0, y242 >= 0 app(z, z') -{ 2 }-> app(15, app(app(1, app(6, x343)), app(6, y240))) :|: x343 >= 0, z' = 1 + 15 + (1 + (1 + 1 + x343) + y240), z = 6, y240 >= 0 app(z, z') -{ 2 }-> app(15, app(15, app(6, z' - 32))) :|: z = 6, z' - 32 >= 0 app(z, z') -{ 2 }-> app(15, 4) :|: z = 6, z' = 1 + 15 + 18 app(z, z') -{ 2 }-> app(15, 3) :|: z = 6, z' = 1 + 15 + 8 app(z, z') -{ 1 }-> app(15, 0) :|: z' - 16 >= 0, z = 6 app(z, z') -{ 1 }-> app(15, 1 + 6 + (z' - 16)) :|: z' - 16 >= 0, z = 6 app(z, z') -{ 1 }-> app(0, z') :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 10) + f) + x app(z, z') -{ 1 }-> app(0, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(0, app(1 + 11 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 7 + x, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 7 + x, app(1 + 11 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(1 + 11 + f, z') :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 12 + 10) + f) + x app(z, z') -{ 1 }-> 4 :|: z' = 18, z = 6 app(z, z') -{ 1 }-> 3 :|: z = 6, z' = 8 app(z, z') -{ 1 }-> 16 :|: z - 15 >= 0, z' = 16 app(z, z') -{ 1 }-> 16 :|: z - 12 >= 0, z' = 16 app(z, z') -{ 0 }-> 0 :|: z >= 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 }-> 19 :|: z = 19 encArg(z) -{ 0 }-> 18 :|: z = 18 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 :|: encode_+ -{ 0 }-> 1 :|: encode_+ -{ 0 }-> 0 :|: encode_- -{ 0 }-> 2 :|: encode_- -{ 0 }-> 0 :|: encode_0 -{ 0 }-> 3 :|: encode_0 -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 4 :|: encode_1 -{ 0 }-> 0 :|: encode_2 -{ 0 }-> 5 :|: encode_2 -{ 0 }-> 0 :|: encode_D -{ 0 }-> 6 :|: encode_D -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_cons -{ 0 }-> 7 :|: encode_cons -{ 0 }-> 0 :|: encode_constant -{ 0 }-> 8 :|: encode_constant -{ 0 }-> 0 :|: encode_div -{ 0 }-> 9 :|: encode_div -{ 0 }-> 0 :|: encode_false -{ 0 }-> 10 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 11 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 12 :|: encode_filter2 -{ 0 }-> 0 :|: encode_ln -{ 0 }-> 13 :|: encode_ln -{ 0 }-> 0 :|: encode_map -{ 0 }-> 14 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 15 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 16 :|: encode_nil -{ 0 }-> 0 :|: encode_pow -{ 0 }-> 17 :|: encode_pow -{ 0 }-> 0 :|: encode_t -{ 0 }-> 18 :|: encode_t -{ 0 }-> 0 :|: encode_true -{ 0 }-> 19 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (29) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_D -> null_encode_D [0] encode_t -> null_encode_t [0] encode_1 -> null_encode_1 [0] encode_constant -> null_encode_constant [0] encode_0 -> null_encode_0 [0] encode_+ -> null_encode_+ [0] encode_* -> null_encode_* [0] encode_- -> null_encode_- [0] encode_minus -> null_encode_minus [0] encode_div -> null_encode_div [0] encode_pow -> null_encode_pow [0] encode_2 -> null_encode_2 [0] encode_ln -> null_encode_ln [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_D, null_encode_t, null_encode_1, null_encode_constant, null_encode_0, null_encode_+, null_encode_*, null_encode_-, null_encode_minus, null_encode_div, null_encode_pow, null_encode_2, null_encode_ln, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(D, t) -> 1 [1] app(D, constant) -> 0 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(D, c_app(c_app(*, x), y)) -> app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y))) [1] app(D, c_app(ln, x)) -> app(app(div, app(D, x)), x) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(D, c_app(minus, x)) -> app(minus, app(D, x)) [1] app(D, c_app(c_app(+, x), y)) -> app(app(+, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(-, x), y)) -> app(app(-, app(D, x)), app(D, y)) [1] app(D, c_app(c_app(pow, x), y)) -> app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(D, c_app(c_app(div, x), y)) -> app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))) [1] encArg(D) -> D [0] encArg(t) -> t [0] encArg(1) -> 1 [0] encArg(constant) -> constant [0] encArg(0) -> 0 [0] encArg(+) -> + [0] encArg(*) -> * [0] encArg(-) -> - [0] encArg(minus) -> minus [0] encArg(div) -> div [0] encArg(pow) -> pow [0] encArg(2) -> 2 [0] encArg(ln) -> ln [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_D -> D [0] encode_t -> t [0] encode_1 -> 1 [0] encode_constant -> constant [0] encode_0 -> 0 [0] encode_+ -> + [0] encode_* -> * [0] encode_- -> - [0] encode_minus -> minus [0] encode_div -> div [0] encode_pow -> pow [0] encode_2 -> 2 [0] encode_ln -> ln [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_D -> null_encode_D [0] encode_t -> null_encode_t [0] encode_1 -> null_encode_1 [0] encode_constant -> null_encode_constant [0] encode_0 -> null_encode_0 [0] encode_+ -> null_encode_+ [0] encode_* -> null_encode_* [0] encode_- -> null_encode_- [0] encode_minus -> null_encode_minus [0] encode_div -> null_encode_div [0] encode_pow -> null_encode_pow [0] encode_2 -> null_encode_2 [0] encode_ln -> null_encode_ln [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app * :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app + :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app - :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_D :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_t :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_constant :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_0 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_+ :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_* :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_- :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_minus :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_div :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_pow :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_ln :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: D:t:1:constant:0:map:c_app:cons:*:+:ln:div:filter2:false:filter:nil:minus:-:pow:true:2:cons_app:null_encArg:null_encode_app:null_encode_D:null_encode_t:null_encode_1:null_encode_constant:null_encode_0:null_encode_+:null_encode_*:null_encode_-:null_encode_minus:null_encode_div:null_encode_pow:null_encode_2:null_encode_ln:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: D => 6 t => 18 1 => 4 constant => 8 0 => 3 map => 14 cons => 7 * => 0 + => 1 ln => 13 div => 9 filter2 => 12 false => 10 filter => 11 nil => 16 minus => 15 - => 2 pow => 17 true => 19 2 => 5 null_encArg => 0 null_encode_app => 0 null_encode_D => 0 null_encode_t => 0 null_encode_1 => 0 null_encode_constant => 0 null_encode_0 => 0 null_encode_+ => 0 null_encode_* => 0 null_encode_- => 0 null_encode_minus => 0 null_encode_div => 0 null_encode_pow => 0 null_encode_2 => 0 null_encode_ln => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_encode_true => 0 null_encode_false => 0 null_app => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> app(app(app(app(12, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 11 + f, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(9, app(6, x)), x) :|: x >= 0, z = 6, z' = 1 + 13 + x app(z, z') -{ 1 }-> app(app(7, x), app(app(11, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 19) + f) + x app(z, z') -{ 1 }-> app(app(7, app(f, x)), app(app(14, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 14 + f, z' = 1 + (1 + 7 + x) + xs app(z, z') -{ 1 }-> app(app(2, app(app(9, app(6, x)), y)), app(app(9, app(app(0, x), app(6, y))), app(app(17, y), 5))) :|: z' = 1 + (1 + 9 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(2, app(6, x)), app(6, y)) :|: x >= 0, y >= 0, z = 6, z' = 1 + (1 + 2 + x) + y app(z, z') -{ 1 }-> app(app(11, f), xs) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 12 + 10) + f) + x app(z, z') -{ 1 }-> app(app(1, app(app(0, y), app(6, x))), app(app(0, x), app(6, y))) :|: z' = 1 + (1 + 0 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(app(0, app(app(0, y), app(app(17, x), app(app(2, y), 4)))), app(6, x))), app(app(0, app(app(0, app(app(17, x), y)), app(13, x))), app(6, y))) :|: z' = 1 + (1 + 17 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(app(1, app(6, x)), app(6, y)) :|: z' = 1 + (1 + 1 + x) + y, x >= 0, y >= 0, z = 6 app(z, z') -{ 1 }-> app(15, app(6, x)) :|: z' = 1 + 15 + x, x >= 0, z = 6 app(z, z') -{ 1 }-> 4 :|: z' = 18, z = 6 app(z, z') -{ 1 }-> 3 :|: z = 6, z' = 8 app(z, z') -{ 1 }-> 16 :|: f >= 0, z = 1 + 14 + f, z' = 16 app(z, z') -{ 1 }-> 16 :|: f >= 0, z = 1 + 11 + f, z' = 16 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 }-> 19 :|: z = 19 encArg(z) -{ 0 }-> 18 :|: z = 18 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 :|: encode_+ -{ 0 }-> 1 :|: encode_+ -{ 0 }-> 0 :|: encode_- -{ 0 }-> 2 :|: encode_- -{ 0 }-> 0 :|: encode_0 -{ 0 }-> 3 :|: encode_0 -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 4 :|: encode_1 -{ 0 }-> 0 :|: encode_2 -{ 0 }-> 5 :|: encode_2 -{ 0 }-> 0 :|: encode_D -{ 0 }-> 6 :|: encode_D -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 7 :|: encode_cons -{ 0 }-> 0 :|: encode_constant -{ 0 }-> 8 :|: encode_constant -{ 0 }-> 0 :|: encode_div -{ 0 }-> 9 :|: encode_div -{ 0 }-> 0 :|: encode_false -{ 0 }-> 10 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 11 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 12 :|: encode_filter2 -{ 0 }-> 0 :|: encode_ln -{ 0 }-> 13 :|: encode_ln -{ 0 }-> 0 :|: encode_map -{ 0 }-> 14 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 15 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 16 :|: encode_nil -{ 0 }-> 0 :|: encode_pow -{ 0 }-> 17 :|: encode_pow -{ 0 }-> 0 :|: encode_t -{ 0 }-> 18 :|: encode_t -{ 0 }-> 0 :|: encode_true -{ 0 }-> 19 :|: encode_true -{ 0 }-> 0 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (33) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(D) -> c ENCARG(t) -> c1 ENCARG(1) -> c2 ENCARG(constant) -> c3 ENCARG(0) -> c4 ENCARG(+) -> c5 ENCARG(*) -> c6 ENCARG(-) -> c7 ENCARG(minus) -> c8 ENCARG(div) -> c9 ENCARG(pow) -> c10 ENCARG(2) -> c11 ENCARG(ln) -> c12 ENCARG(map) -> c13 ENCARG(nil) -> c14 ENCARG(cons) -> c15 ENCARG(filter) -> c16 ENCARG(filter2) -> c17 ENCARG(true) -> c18 ENCARG(false) -> c19 ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c21(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_D -> c22 ENCODE_T -> c23 ENCODE_1 -> c24 ENCODE_CONSTANT -> c25 ENCODE_0 -> c26 ENCODE_+ -> c27 ENCODE_* -> c28 ENCODE_- -> c29 ENCODE_MINUS -> c30 ENCODE_DIV -> c31 ENCODE_POW -> c32 ENCODE_2 -> c33 ENCODE_LN -> c34 ENCODE_MAP -> c35 ENCODE_NIL -> c36 ENCODE_CONS -> c37 ENCODE_FILTER -> c38 ENCODE_FILTER2 -> c39 ENCODE_TRUE -> c40 ENCODE_FALSE -> c41 APP(D, t) -> c42 APP(D, constant) -> c43 APP(D, app(app(+, z0), z1)) -> c44(APP(app(+, app(D, z0)), app(D, z1)), APP(+, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))), APP(+, app(app(*, z1), app(D, z0))), APP(app(*, z1), app(D, z0)), APP(*, z1), APP(D, z0), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(app(-, app(D, z0)), app(D, z1)), APP(-, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(minus, app(D, z0)), APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))), APP(-, app(app(div, app(D, z0)), z1)), APP(app(div, app(D, z0)), z1), APP(div, app(D, z0)), APP(D, z0), APP(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)), APP(div, app(app(*, z0), app(D, z1))), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1), APP(app(pow, z1), 2), APP(pow, z1)) APP(D, app(ln, z0)) -> c49(APP(app(div, app(D, z0)), z0), APP(div, app(D, z0)), APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))), APP(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), APP(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0)), APP(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), APP(app(*, z1), app(app(pow, z0), app(app(-, z1), 1))), APP(*, z1), APP(app(pow, z0), app(app(-, z1), 1)), APP(pow, z0), APP(app(-, z1), 1), APP(-, z1), APP(D, z0), APP(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)), APP(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), APP(app(*, app(app(pow, z0), z1)), app(ln, z0)), APP(*, app(app(pow, z0), z1)), APP(app(pow, z0), z1), APP(pow, z0), APP(ln, z0), APP(D, z1)) APP(app(map, z0), nil) -> c51 APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c53 APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(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) -> c55(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(D, app(app(+, z0), z1)) -> c44(APP(app(+, app(D, z0)), app(D, z1)), APP(+, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))), APP(+, app(app(*, z1), app(D, z0))), APP(app(*, z1), app(D, z0)), APP(*, z1), APP(D, z0), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(app(-, app(D, z0)), app(D, z1)), APP(-, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(minus, app(D, z0)), APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))), APP(-, app(app(div, app(D, z0)), z1)), APP(app(div, app(D, z0)), z1), APP(div, app(D, z0)), APP(D, z0), APP(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)), APP(div, app(app(*, z0), app(D, z1))), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1), APP(app(pow, z1), 2), APP(pow, z1)) APP(D, app(ln, z0)) -> c49(APP(app(div, app(D, z0)), z0), APP(div, app(D, z0)), APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))), APP(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), APP(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0)), APP(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), APP(app(*, z1), app(app(pow, z0), app(app(-, z1), 1))), APP(*, z1), APP(app(pow, z0), app(app(-, z1), 1)), APP(pow, z0), APP(app(-, z1), 1), APP(-, z1), APP(D, z0), APP(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)), APP(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), APP(app(*, app(app(pow, z0), z1)), app(ln, z0)), APP(*, app(app(pow, z0), z1)), APP(app(pow, z0), z1), APP(pow, z0), APP(ln, z0), APP(D, z1)) APP(app(map, z0), nil) -> c51 APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c53 APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(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) -> c55(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_D, encode_t, encode_1, encode_constant, encode_0, encode_+, encode_*, encode_-, encode_minus, encode_div, encode_pow, encode_2, encode_ln, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_D, ENCODE_T, ENCODE_1, ENCODE_CONSTANT, ENCODE_0, ENCODE_+, ENCODE_*, ENCODE_-, ENCODE_MINUS, ENCODE_DIV, ENCODE_POW, ENCODE_2, ENCODE_LN, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_FILTER2, ENCODE_TRUE, ENCODE_FALSE, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20_3, c21_3, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44_4, c45_8, c46_4, c47_2, c48_12, c49_3, c50_19, c51, c52_5, c53, c54_5, c55_4, c56_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 40 trailing nodes: ENCODE_* -> c28 ENCODE_DIV -> c31 ENCARG(ln) -> c12 ENCARG(cons) -> c15 ENCARG(map) -> c13 ENCODE_MAP -> c35 ENCODE_FILTER2 -> c39 ENCARG(t) -> c1 ENCARG(true) -> c18 ENCARG(false) -> c19 ENCODE_0 -> c26 ENCARG(*) -> c6 ENCARG(div) -> c9 ENCODE_FILTER -> c38 ENCARG(2) -> c11 ENCODE_+ -> c27 ENCODE_LN -> c34 ENCODE_CONS -> c37 ENCODE_MINUS -> c30 ENCODE_- -> c29 ENCARG(D) -> c ENCODE_D -> c22 ENCARG(1) -> c2 ENCODE_FALSE -> c41 ENCODE_T -> c23 ENCARG(+) -> c5 ENCARG(-) -> c7 ENCARG(pow) -> c10 ENCARG(constant) -> c3 ENCODE_POW -> c32 ENCARG(nil) -> c14 ENCARG(filter2) -> c17 ENCODE_CONSTANT -> c25 ENCODE_1 -> c24 ENCARG(filter) -> c16 ENCODE_NIL -> c36 ENCARG(minus) -> c8 ENCODE_2 -> c33 ENCARG(0) -> c4 ENCODE_TRUE -> c40 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c21(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(D, t) -> c42 APP(D, constant) -> c43 APP(D, app(app(+, z0), z1)) -> c44(APP(app(+, app(D, z0)), app(D, z1)), APP(+, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))), APP(+, app(app(*, z1), app(D, z0))), APP(app(*, z1), app(D, z0)), APP(*, z1), APP(D, z0), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(app(-, app(D, z0)), app(D, z1)), APP(-, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(minus, app(D, z0)), APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))), APP(-, app(app(div, app(D, z0)), z1)), APP(app(div, app(D, z0)), z1), APP(div, app(D, z0)), APP(D, z0), APP(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)), APP(div, app(app(*, z0), app(D, z1))), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1), APP(app(pow, z1), 2), APP(pow, z1)) APP(D, app(ln, z0)) -> c49(APP(app(div, app(D, z0)), z0), APP(div, app(D, z0)), APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))), APP(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), APP(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0)), APP(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), APP(app(*, z1), app(app(pow, z0), app(app(-, z1), 1))), APP(*, z1), APP(app(pow, z0), app(app(-, z1), 1)), APP(pow, z0), APP(app(-, z1), 1), APP(-, z1), APP(D, z0), APP(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)), APP(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), APP(app(*, app(app(pow, z0), z1)), app(ln, z0)), APP(*, app(app(pow, z0), z1)), APP(app(pow, z0), z1), APP(pow, z0), APP(ln, z0), APP(D, z1)) APP(app(map, z0), nil) -> c51 APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c53 APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(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) -> c55(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(D, app(app(+, z0), z1)) -> c44(APP(app(+, app(D, z0)), app(D, z1)), APP(+, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))), APP(+, app(app(*, z1), app(D, z0))), APP(app(*, z1), app(D, z0)), APP(*, z1), APP(D, z0), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(app(-, app(D, z0)), app(D, z1)), APP(-, app(D, z0)), APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(minus, app(D, z0)), APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))), APP(-, app(app(div, app(D, z0)), z1)), APP(app(div, app(D, z0)), z1), APP(div, app(D, z0)), APP(D, z0), APP(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)), APP(div, app(app(*, z0), app(D, z1))), APP(app(*, z0), app(D, z1)), APP(*, z0), APP(D, z1), APP(app(pow, z1), 2), APP(pow, z1)) APP(D, app(ln, z0)) -> c49(APP(app(div, app(D, z0)), z0), APP(div, app(D, z0)), APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))), APP(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), APP(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0)), APP(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), APP(app(*, z1), app(app(pow, z0), app(app(-, z1), 1))), APP(*, z1), APP(app(pow, z0), app(app(-, z1), 1)), APP(pow, z0), APP(app(-, z1), 1), APP(-, z1), APP(D, z0), APP(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)), APP(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), APP(app(*, app(app(pow, z0), z1)), app(ln, z0)), APP(*, app(app(pow, z0), z1)), APP(app(pow, z0), z1), APP(pow, z0), APP(ln, z0), APP(D, z1)) APP(app(map, z0), nil) -> c51 APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c53 APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(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) -> c55(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_D, encode_t, encode_1, encode_constant, encode_0, encode_+, encode_*, encode_-, encode_minus, encode_div, encode_pow, encode_2, encode_ln, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c20_3, c21_3, c42, c43, c44_4, c45_8, c46_4, c47_2, c48_12, c49_3, c50_19, c51, c52_5, c53, c54_5, c55_4, c56_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 50 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c21(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_D, encode_t, encode_1, encode_constant, encode_0, encode_+, encode_*, encode_-, encode_minus, encode_div, encode_pow, encode_2, encode_ln, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c20_3, c21_3, c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_1 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(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(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_D, encode_t, encode_1, encode_constant, encode_0, encode_+, encode_*, encode_-, encode_minus, encode_div, encode_pow, encode_2, encode_ln, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c20_3, c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_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(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_D, encode_t, encode_1, encode_constant, encode_0, encode_+, encode_*, encode_-, encode_minus, encode_div, encode_pow, encode_2, encode_ln, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c20_3, c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_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_D -> D encode_t -> t encode_1 -> 1 encode_constant -> constant encode_0 -> 0 encode_+ -> + encode_* -> * encode_- -> - encode_minus -> minus encode_div -> div encode_pow -> pow encode_2 -> 2 encode_ln -> ln encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(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: c20_3, c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_1, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c20(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0), ENCARG(D)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0), ENCARG(t)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0), ENCARG(1)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0), ENCARG(constant)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0), ENCARG(+)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0), ENCARG(*)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0), ENCARG(-)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0), ENCARG(div)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0), ENCARG(pow)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0), ENCARG(2)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0), ENCARG(ln)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(D), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(APP(t, encArg(x1)), ENCARG(t), ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(APP(1, encArg(x1)), ENCARG(1), ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(APP(constant, encArg(x1)), ENCARG(constant), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(APP(+, encArg(x1)), ENCARG(+), ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(APP(*, encArg(x1)), ENCARG(*), ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(APP(-, encArg(x1)), ENCARG(-), ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(APP(div, encArg(x1)), ENCARG(div), ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(APP(pow, encArg(x1)), ENCARG(pow), ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(APP(2, encArg(x1)), ENCARG(2), ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(APP(ln, encArg(x1)), ENCARG(ln), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0), ENCARG(D)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0), ENCARG(t)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0), ENCARG(1)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0), ENCARG(constant)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0), ENCARG(+)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0), ENCARG(*)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0), ENCARG(-)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0), ENCARG(div)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0), ENCARG(pow)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0), ENCARG(2)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0), ENCARG(ln)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(D), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(APP(t, encArg(x1)), ENCARG(t), ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(APP(1, encArg(x1)), ENCARG(1), ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(APP(constant, encArg(x1)), ENCARG(constant), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(APP(+, encArg(x1)), ENCARG(+), ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(APP(*, encArg(x1)), ENCARG(*), ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(APP(-, encArg(x1)), ENCARG(-), ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(APP(div, encArg(x1)), ENCARG(div), ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(APP(pow, encArg(x1)), ENCARG(pow), ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(APP(2, encArg(x1)), ENCARG(2), ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(APP(ln, encArg(x1)), ENCARG(ln), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_1, c_1, c20_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 59 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c54_2, c55_1, c56_1, c_1, c20_3, c20_2, c20_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c54(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by APP(app(filter, D), app(app(cons, t), x2)) -> c54(APP(app(app(app(filter2, 1), D), t), x2), APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(app(app(app(filter2, 0), D), constant), x2), APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(D, z0)), app(D, z1))), D), app(app(+, z0), z1)), x2), APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1)))), D), app(app(*, z0), z1)), x2), APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(D, z0)), app(D, z1))), D), app(app(-, z0), z1)), x2), APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(app(app(app(filter2, app(minus, app(D, z0))), D), app(minus, z0)), x2), APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)))), D), app(app(div, z0), z1)), x2), APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(app(app(app(filter2, app(app(div, app(D, z0)), z0)), D), app(ln, z0)), x2), APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)))), D), app(app(pow, z0), z1)), x2), APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, D), app(app(cons, t), x2)) -> c54(APP(app(app(app(filter2, 1), D), t), x2), APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(app(app(app(filter2, 0), D), constant), x2), APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(D, z0)), app(D, z1))), D), app(app(+, z0), z1)), x2), APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1)))), D), app(app(*, z0), z1)), x2), APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(D, z0)), app(D, z1))), D), app(app(-, z0), z1)), x2), APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(app(app(app(filter2, app(minus, app(D, z0))), D), app(minus, z0)), x2), APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)))), D), app(app(div, z0), z1)), x2), APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(app(app(app(filter2, app(app(div, app(D, z0)), z0)), D), app(ln, z0)), x2), APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)))), D), app(app(pow, z0), z1)), x2), APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, D), app(app(cons, t), x2)) -> c54(APP(app(app(app(filter2, 1), D), t), x2), APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(app(app(app(filter2, 0), D), constant), x2), APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(D, z0)), app(D, z1))), D), app(app(+, z0), z1)), x2), APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1)))), D), app(app(*, z0), z1)), x2), APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(D, z0)), app(D, z1))), D), app(app(-, z0), z1)), x2), APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(app(app(app(filter2, app(minus, app(D, z0))), D), app(minus, z0)), x2), APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2)))), D), app(app(div, z0), z1)), x2), APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(app(app(app(filter2, app(app(div, app(D, z0)), z0)), D), app(ln, z0)), x2), APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(app(app(app(filter2, app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1)))), D), app(app(pow, z0), z1)), x2), APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c_1, c20_3, c20_2, c20_1, c54_2 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c_1, c20_3, c20_2, c20_1, c54_2, c54_1 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, encArg(x1))) ENCODE_APP(t, x1) -> c(APP(t, encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(constant, x1) -> c(APP(constant, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(+, x1) -> c(APP(+, encArg(x1))) ENCODE_APP(*, x1) -> c(APP(*, encArg(x1))) ENCODE_APP(-, x1) -> c(APP(-, encArg(x1))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(div, x1) -> c(APP(div, encArg(x1))) ENCODE_APP(pow, x1) -> c(APP(pow, encArg(x1))) ENCODE_APP(2, x1) -> c(APP(2, encArg(x1))) ENCODE_APP(ln, x1) -> c(APP(ln, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, encArg(x1))) ENCODE_APP(t, x1) -> c(APP(t, encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(constant, x1) -> c(APP(constant, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(+, x1) -> c(APP(+, encArg(x1))) ENCODE_APP(*, x1) -> c(APP(*, encArg(x1))) ENCODE_APP(-, x1) -> c(APP(-, encArg(x1))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(div, x1) -> c(APP(div, encArg(x1))) ENCODE_APP(pow, x1) -> c(APP(pow, encArg(x1))) ENCODE_APP(2, x1) -> c(APP(2, encArg(x1))) ENCODE_APP(ln, x1) -> c(APP(ln, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_3, c20_2, c20_1, c54_2, c54_1, c_1 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 19 trailing nodes: ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(2, x1) -> c(APP(2, encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(constant, x1) -> c(APP(constant, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(+, x1) -> c(APP(+, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(t, x1) -> c(APP(t, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(ln, x1) -> c(APP(ln, encArg(x1))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(div, x1) -> c(APP(div, encArg(x1))) ENCODE_APP(-, x1) -> c(APP(-, encArg(x1))) ENCODE_APP(pow, x1) -> c(APP(pow, encArg(x1))) ENCODE_APP(*, x1) -> c(APP(*, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_3, c20_2, c20_1, c54_2, c54_1, c_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c20(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(D), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(APP(t, app(encArg(x1), encArg(x2))), ENCARG(t), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(APP(1, app(encArg(x1), encArg(x2))), ENCARG(1), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(APP(constant, app(encArg(x1), encArg(x2))), ENCARG(constant), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(APP(+, app(encArg(x1), encArg(x2))), ENCARG(+), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(APP(*, app(encArg(x1), encArg(x2))), ENCARG(*), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(APP(-, app(encArg(x1), encArg(x2))), ENCARG(-), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(APP(div, app(encArg(x1), encArg(x2))), ENCARG(div), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(APP(pow, app(encArg(x1), encArg(x2))), ENCARG(pow), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(APP(2, app(encArg(x1), encArg(x2))), ENCARG(2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(APP(ln, app(encArg(x1), encArg(x2))), ENCARG(ln), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(D), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(APP(t, app(encArg(x1), encArg(x2))), ENCARG(t), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(APP(1, app(encArg(x1), encArg(x2))), ENCARG(1), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(APP(constant, app(encArg(x1), encArg(x2))), ENCARG(constant), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(APP(+, app(encArg(x1), encArg(x2))), ENCARG(+), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(APP(*, app(encArg(x1), encArg(x2))), ENCARG(*), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(APP(-, app(encArg(x1), encArg(x2))), ENCARG(-), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(APP(div, app(encArg(x1), encArg(x2))), ENCARG(div), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(APP(pow, app(encArg(x1), encArg(x2))), ENCARG(pow), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(APP(2, app(encArg(x1), encArg(x2))), ENCARG(2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(APP(ln, app(encArg(x1), encArg(x2))), ENCARG(ln), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_3, c20_2, c20_1, c54_2, c54_1, c_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 39 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_3, c20_2, c20_1, c54_2, c54_1, c_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c20(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1)), ENCARG(D)) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1)), ENCARG(t)) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1)), ENCARG(1)) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1)), ENCARG(constant)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1)), ENCARG(+)) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1)), ENCARG(*)) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1)), ENCARG(-)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus)) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)), ENCARG(div)) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1)), ENCARG(pow)) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1)), ENCARG(2)) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1)), ENCARG(ln)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c20(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, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(APP(app(t, encArg(x1)), encArg(x2)), ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(APP(app(1, encArg(x1)), encArg(x2)), ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(APP(app(constant, encArg(x1)), encArg(x2)), ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(APP(app(+, encArg(x1)), encArg(x2)), ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(APP(app(*, encArg(x1)), encArg(x2)), ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(APP(app(-, encArg(x1)), encArg(x2)), ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(APP(app(pow, encArg(x1)), encArg(x2)), ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(APP(app(2, encArg(x1)), encArg(x2)), ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(APP(app(ln, encArg(x1)), encArg(x2)), ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c20(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1)), ENCARG(D)) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1)), ENCARG(t)) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1)), ENCARG(1)) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1)), ENCARG(constant)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1)), ENCARG(+)) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1)), ENCARG(*)) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1)), ENCARG(-)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus)) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1)), ENCARG(div)) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1)), ENCARG(pow)) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1)), ENCARG(2)) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1)), ENCARG(ln)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(APP(app(t, encArg(x1)), encArg(x2)), ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(APP(app(1, encArg(x1)), encArg(x2)), ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(APP(app(constant, encArg(x1)), encArg(x2)), ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(APP(app(+, encArg(x1)), encArg(x2)), ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(APP(app(*, encArg(x1)), encArg(x2)), ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(APP(app(-, encArg(x1)), encArg(x2)), ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(APP(app(div, encArg(x1)), encArg(x2)), ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(APP(app(pow, encArg(x1)), encArg(x2)), ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(APP(app(2, encArg(x1)), encArg(x2)), ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(APP(app(ln, encArg(x1)), encArg(x2)), ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c20(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 37 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, D)) -> c20(APP(encArg(x0), D), ENCARG(x0)) by ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(t, D)) -> c20(APP(t, D), ENCARG(t)) ENCARG(cons_app(1, D)) -> c20(APP(1, D), ENCARG(1)) ENCARG(cons_app(constant, D)) -> c20(APP(constant, D), ENCARG(constant)) ENCARG(cons_app(0, D)) -> c20(APP(0, D), ENCARG(0)) ENCARG(cons_app(+, D)) -> c20(APP(+, D), ENCARG(+)) ENCARG(cons_app(*, D)) -> c20(APP(*, D), ENCARG(*)) ENCARG(cons_app(-, D)) -> c20(APP(-, D), ENCARG(-)) ENCARG(cons_app(minus, D)) -> c20(APP(minus, D), ENCARG(minus)) ENCARG(cons_app(div, D)) -> c20(APP(div, D), ENCARG(div)) ENCARG(cons_app(pow, D)) -> c20(APP(pow, D), ENCARG(pow)) ENCARG(cons_app(2, D)) -> c20(APP(2, D), ENCARG(2)) ENCARG(cons_app(ln, D)) -> c20(APP(ln, D), ENCARG(ln)) ENCARG(cons_app(map, D)) -> c20(APP(map, D), ENCARG(map)) ENCARG(cons_app(nil, D)) -> c20(APP(nil, D), ENCARG(nil)) ENCARG(cons_app(cons, D)) -> c20(APP(cons, D), ENCARG(cons)) ENCARG(cons_app(filter, D)) -> c20(APP(filter, D), ENCARG(filter)) ENCARG(cons_app(filter2, D)) -> c20(APP(filter2, D), ENCARG(filter2)) ENCARG(cons_app(true, D)) -> c20(APP(true, D), ENCARG(true)) ENCARG(cons_app(false, D)) -> c20(APP(false, D), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), D)) -> c20(APP(app(encArg(z0), encArg(z1)), D), ENCARG(cons_app(z0, z1))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(t, D)) -> c20(APP(t, D), ENCARG(t)) ENCARG(cons_app(1, D)) -> c20(APP(1, D), ENCARG(1)) ENCARG(cons_app(constant, D)) -> c20(APP(constant, D), ENCARG(constant)) ENCARG(cons_app(0, D)) -> c20(APP(0, D), ENCARG(0)) ENCARG(cons_app(+, D)) -> c20(APP(+, D), ENCARG(+)) ENCARG(cons_app(*, D)) -> c20(APP(*, D), ENCARG(*)) ENCARG(cons_app(-, D)) -> c20(APP(-, D), ENCARG(-)) ENCARG(cons_app(minus, D)) -> c20(APP(minus, D), ENCARG(minus)) ENCARG(cons_app(div, D)) -> c20(APP(div, D), ENCARG(div)) ENCARG(cons_app(pow, D)) -> c20(APP(pow, D), ENCARG(pow)) ENCARG(cons_app(2, D)) -> c20(APP(2, D), ENCARG(2)) ENCARG(cons_app(ln, D)) -> c20(APP(ln, D), ENCARG(ln)) ENCARG(cons_app(map, D)) -> c20(APP(map, D), ENCARG(map)) ENCARG(cons_app(nil, D)) -> c20(APP(nil, D), ENCARG(nil)) ENCARG(cons_app(cons, D)) -> c20(APP(cons, D), ENCARG(cons)) ENCARG(cons_app(filter, D)) -> c20(APP(filter, D), ENCARG(filter)) ENCARG(cons_app(filter2, D)) -> c20(APP(filter2, D), ENCARG(filter2)) ENCARG(cons_app(true, D)) -> c20(APP(true, D), ENCARG(true)) ENCARG(cons_app(false, D)) -> c20(APP(false, D), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(filter, D)) -> c20(APP(filter, D), ENCARG(filter)) ENCARG(cons_app(0, D)) -> c20(APP(0, D), ENCARG(0)) ENCARG(cons_app(ln, D)) -> c20(APP(ln, D), ENCARG(ln)) ENCARG(cons_app(nil, D)) -> c20(APP(nil, D), ENCARG(nil)) ENCARG(cons_app(t, D)) -> c20(APP(t, D), ENCARG(t)) ENCARG(cons_app(cons, D)) -> c20(APP(cons, D), ENCARG(cons)) ENCARG(cons_app(div, D)) -> c20(APP(div, D), ENCARG(div)) ENCARG(cons_app(true, D)) -> c20(APP(true, D), ENCARG(true)) ENCARG(cons_app(+, D)) -> c20(APP(+, D), ENCARG(+)) ENCARG(cons_app(minus, D)) -> c20(APP(minus, D), ENCARG(minus)) ENCARG(cons_app(-, D)) -> c20(APP(-, D), ENCARG(-)) ENCARG(cons_app(constant, D)) -> c20(APP(constant, D), ENCARG(constant)) ENCARG(cons_app(2, D)) -> c20(APP(2, D), ENCARG(2)) ENCARG(cons_app(*, D)) -> c20(APP(*, D), ENCARG(*)) ENCARG(cons_app(1, D)) -> c20(APP(1, D), ENCARG(1)) ENCARG(cons_app(pow, D)) -> c20(APP(pow, D), ENCARG(pow)) ENCARG(cons_app(map, D)) -> c20(APP(map, D), ENCARG(map)) ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(filter2, D)) -> c20(APP(filter2, D), ENCARG(filter2)) ENCARG(cons_app(false, D)) -> c20(APP(false, D), ENCARG(false)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, t)) -> c20(APP(encArg(x0), t), ENCARG(x0)) by ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(D)) ENCARG(cons_app(t, t)) -> c20(APP(t, t), ENCARG(t)) ENCARG(cons_app(1, t)) -> c20(APP(1, t), ENCARG(1)) ENCARG(cons_app(constant, t)) -> c20(APP(constant, t), ENCARG(constant)) ENCARG(cons_app(0, t)) -> c20(APP(0, t), ENCARG(0)) ENCARG(cons_app(+, t)) -> c20(APP(+, t), ENCARG(+)) ENCARG(cons_app(*, t)) -> c20(APP(*, t), ENCARG(*)) ENCARG(cons_app(-, t)) -> c20(APP(-, t), ENCARG(-)) ENCARG(cons_app(minus, t)) -> c20(APP(minus, t), ENCARG(minus)) ENCARG(cons_app(div, t)) -> c20(APP(div, t), ENCARG(div)) ENCARG(cons_app(pow, t)) -> c20(APP(pow, t), ENCARG(pow)) ENCARG(cons_app(2, t)) -> c20(APP(2, t), ENCARG(2)) ENCARG(cons_app(ln, t)) -> c20(APP(ln, t), ENCARG(ln)) ENCARG(cons_app(map, t)) -> c20(APP(map, t), ENCARG(map)) ENCARG(cons_app(nil, t)) -> c20(APP(nil, t), ENCARG(nil)) ENCARG(cons_app(cons, t)) -> c20(APP(cons, t), ENCARG(cons)) ENCARG(cons_app(filter, t)) -> c20(APP(filter, t), ENCARG(filter)) ENCARG(cons_app(filter2, t)) -> c20(APP(filter2, t), ENCARG(filter2)) ENCARG(cons_app(true, t)) -> c20(APP(true, t), ENCARG(true)) ENCARG(cons_app(false, t)) -> c20(APP(false, t), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), t)) -> c20(APP(app(encArg(z0), encArg(z1)), t), ENCARG(cons_app(z0, z1))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(D)) ENCARG(cons_app(t, t)) -> c20(APP(t, t), ENCARG(t)) ENCARG(cons_app(1, t)) -> c20(APP(1, t), ENCARG(1)) ENCARG(cons_app(constant, t)) -> c20(APP(constant, t), ENCARG(constant)) ENCARG(cons_app(0, t)) -> c20(APP(0, t), ENCARG(0)) ENCARG(cons_app(+, t)) -> c20(APP(+, t), ENCARG(+)) ENCARG(cons_app(*, t)) -> c20(APP(*, t), ENCARG(*)) ENCARG(cons_app(-, t)) -> c20(APP(-, t), ENCARG(-)) ENCARG(cons_app(minus, t)) -> c20(APP(minus, t), ENCARG(minus)) ENCARG(cons_app(div, t)) -> c20(APP(div, t), ENCARG(div)) ENCARG(cons_app(pow, t)) -> c20(APP(pow, t), ENCARG(pow)) ENCARG(cons_app(2, t)) -> c20(APP(2, t), ENCARG(2)) ENCARG(cons_app(ln, t)) -> c20(APP(ln, t), ENCARG(ln)) ENCARG(cons_app(map, t)) -> c20(APP(map, t), ENCARG(map)) ENCARG(cons_app(nil, t)) -> c20(APP(nil, t), ENCARG(nil)) ENCARG(cons_app(cons, t)) -> c20(APP(cons, t), ENCARG(cons)) ENCARG(cons_app(filter, t)) -> c20(APP(filter, t), ENCARG(filter)) ENCARG(cons_app(filter2, t)) -> c20(APP(filter2, t), ENCARG(filter2)) ENCARG(cons_app(true, t)) -> c20(APP(true, t), ENCARG(true)) ENCARG(cons_app(false, t)) -> c20(APP(false, t), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 19 trailing nodes: ENCARG(cons_app(pow, t)) -> c20(APP(pow, t), ENCARG(pow)) ENCARG(cons_app(*, t)) -> c20(APP(*, t), ENCARG(*)) ENCARG(cons_app(minus, t)) -> c20(APP(minus, t), ENCARG(minus)) ENCARG(cons_app(0, t)) -> c20(APP(0, t), ENCARG(0)) ENCARG(cons_app(t, t)) -> c20(APP(t, t), ENCARG(t)) ENCARG(cons_app(ln, t)) -> c20(APP(ln, t), ENCARG(ln)) ENCARG(cons_app(-, t)) -> c20(APP(-, t), ENCARG(-)) ENCARG(cons_app(constant, t)) -> c20(APP(constant, t), ENCARG(constant)) ENCARG(cons_app(2, t)) -> c20(APP(2, t), ENCARG(2)) ENCARG(cons_app(filter2, t)) -> c20(APP(filter2, t), ENCARG(filter2)) ENCARG(cons_app(true, t)) -> c20(APP(true, t), ENCARG(true)) ENCARG(cons_app(nil, t)) -> c20(APP(nil, t), ENCARG(nil)) ENCARG(cons_app(map, t)) -> c20(APP(map, t), ENCARG(map)) ENCARG(cons_app(false, t)) -> c20(APP(false, t), ENCARG(false)) ENCARG(cons_app(div, t)) -> c20(APP(div, t), ENCARG(div)) ENCARG(cons_app(1, t)) -> c20(APP(1, t), ENCARG(1)) ENCARG(cons_app(+, t)) -> c20(APP(+, t), ENCARG(+)) ENCARG(cons_app(cons, t)) -> c20(APP(cons, t), ENCARG(cons)) ENCARG(cons_app(filter, t)) -> c20(APP(filter, t), ENCARG(filter)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(D)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 1)) -> c20(APP(encArg(x0), 1), ENCARG(x0)) by ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(D)) ENCARG(cons_app(t, 1)) -> c20(APP(t, 1), ENCARG(t)) ENCARG(cons_app(1, 1)) -> c20(APP(1, 1), ENCARG(1)) ENCARG(cons_app(constant, 1)) -> c20(APP(constant, 1), ENCARG(constant)) ENCARG(cons_app(0, 1)) -> c20(APP(0, 1), ENCARG(0)) ENCARG(cons_app(+, 1)) -> c20(APP(+, 1), ENCARG(+)) ENCARG(cons_app(*, 1)) -> c20(APP(*, 1), ENCARG(*)) ENCARG(cons_app(-, 1)) -> c20(APP(-, 1), ENCARG(-)) ENCARG(cons_app(minus, 1)) -> c20(APP(minus, 1), ENCARG(minus)) ENCARG(cons_app(div, 1)) -> c20(APP(div, 1), ENCARG(div)) ENCARG(cons_app(pow, 1)) -> c20(APP(pow, 1), ENCARG(pow)) ENCARG(cons_app(2, 1)) -> c20(APP(2, 1), ENCARG(2)) ENCARG(cons_app(ln, 1)) -> c20(APP(ln, 1), ENCARG(ln)) ENCARG(cons_app(map, 1)) -> c20(APP(map, 1), ENCARG(map)) ENCARG(cons_app(nil, 1)) -> c20(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(cons, 1)) -> c20(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(filter, 1)) -> c20(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(filter2, 1)) -> c20(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(true, 1)) -> c20(APP(true, 1), ENCARG(true)) ENCARG(cons_app(false, 1)) -> c20(APP(false, 1), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), 1)) -> c20(APP(app(encArg(z0), encArg(z1)), 1), ENCARG(cons_app(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(D)) ENCARG(cons_app(t, 1)) -> c20(APP(t, 1), ENCARG(t)) ENCARG(cons_app(1, 1)) -> c20(APP(1, 1), ENCARG(1)) ENCARG(cons_app(constant, 1)) -> c20(APP(constant, 1), ENCARG(constant)) ENCARG(cons_app(0, 1)) -> c20(APP(0, 1), ENCARG(0)) ENCARG(cons_app(+, 1)) -> c20(APP(+, 1), ENCARG(+)) ENCARG(cons_app(*, 1)) -> c20(APP(*, 1), ENCARG(*)) ENCARG(cons_app(-, 1)) -> c20(APP(-, 1), ENCARG(-)) ENCARG(cons_app(minus, 1)) -> c20(APP(minus, 1), ENCARG(minus)) ENCARG(cons_app(div, 1)) -> c20(APP(div, 1), ENCARG(div)) ENCARG(cons_app(pow, 1)) -> c20(APP(pow, 1), ENCARG(pow)) ENCARG(cons_app(2, 1)) -> c20(APP(2, 1), ENCARG(2)) ENCARG(cons_app(ln, 1)) -> c20(APP(ln, 1), ENCARG(ln)) ENCARG(cons_app(map, 1)) -> c20(APP(map, 1), ENCARG(map)) ENCARG(cons_app(nil, 1)) -> c20(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(cons, 1)) -> c20(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(filter, 1)) -> c20(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(filter2, 1)) -> c20(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(true, 1)) -> c20(APP(true, 1), ENCARG(true)) ENCARG(cons_app(false, 1)) -> c20(APP(false, 1), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(2, 1)) -> c20(APP(2, 1), ENCARG(2)) ENCARG(cons_app(0, 1)) -> c20(APP(0, 1), ENCARG(0)) ENCARG(cons_app(map, 1)) -> c20(APP(map, 1), ENCARG(map)) ENCARG(cons_app(t, 1)) -> c20(APP(t, 1), ENCARG(t)) ENCARG(cons_app(minus, 1)) -> c20(APP(minus, 1), ENCARG(minus)) ENCARG(cons_app(cons, 1)) -> c20(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(-, 1)) -> c20(APP(-, 1), ENCARG(-)) ENCARG(cons_app(constant, 1)) -> c20(APP(constant, 1), ENCARG(constant)) ENCARG(cons_app(pow, 1)) -> c20(APP(pow, 1), ENCARG(pow)) ENCARG(cons_app(div, 1)) -> c20(APP(div, 1), ENCARG(div)) ENCARG(cons_app(filter, 1)) -> c20(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(true, 1)) -> c20(APP(true, 1), ENCARG(true)) ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(D)) ENCARG(cons_app(false, 1)) -> c20(APP(false, 1), ENCARG(false)) ENCARG(cons_app(*, 1)) -> c20(APP(*, 1), ENCARG(*)) ENCARG(cons_app(ln, 1)) -> c20(APP(ln, 1), ENCARG(ln)) ENCARG(cons_app(+, 1)) -> c20(APP(+, 1), ENCARG(+)) ENCARG(cons_app(nil, 1)) -> c20(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(filter2, 1)) -> c20(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(1, 1)) -> c20(APP(1, 1), ENCARG(1)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, constant)) -> c20(APP(encArg(x0), constant), ENCARG(x0)) by ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(D)) ENCARG(cons_app(t, constant)) -> c20(APP(t, constant), ENCARG(t)) ENCARG(cons_app(1, constant)) -> c20(APP(1, constant), ENCARG(1)) ENCARG(cons_app(constant, constant)) -> c20(APP(constant, constant), ENCARG(constant)) ENCARG(cons_app(0, constant)) -> c20(APP(0, constant), ENCARG(0)) ENCARG(cons_app(+, constant)) -> c20(APP(+, constant), ENCARG(+)) ENCARG(cons_app(*, constant)) -> c20(APP(*, constant), ENCARG(*)) ENCARG(cons_app(-, constant)) -> c20(APP(-, constant), ENCARG(-)) ENCARG(cons_app(minus, constant)) -> c20(APP(minus, constant), ENCARG(minus)) ENCARG(cons_app(div, constant)) -> c20(APP(div, constant), ENCARG(div)) ENCARG(cons_app(pow, constant)) -> c20(APP(pow, constant), ENCARG(pow)) ENCARG(cons_app(2, constant)) -> c20(APP(2, constant), ENCARG(2)) ENCARG(cons_app(ln, constant)) -> c20(APP(ln, constant), ENCARG(ln)) ENCARG(cons_app(map, constant)) -> c20(APP(map, constant), ENCARG(map)) ENCARG(cons_app(nil, constant)) -> c20(APP(nil, constant), ENCARG(nil)) ENCARG(cons_app(cons, constant)) -> c20(APP(cons, constant), ENCARG(cons)) ENCARG(cons_app(filter, constant)) -> c20(APP(filter, constant), ENCARG(filter)) ENCARG(cons_app(filter2, constant)) -> c20(APP(filter2, constant), ENCARG(filter2)) ENCARG(cons_app(true, constant)) -> c20(APP(true, constant), ENCARG(true)) ENCARG(cons_app(false, constant)) -> c20(APP(false, constant), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), constant)) -> c20(APP(app(encArg(z0), encArg(z1)), constant), ENCARG(cons_app(z0, z1))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(D)) ENCARG(cons_app(t, constant)) -> c20(APP(t, constant), ENCARG(t)) ENCARG(cons_app(1, constant)) -> c20(APP(1, constant), ENCARG(1)) ENCARG(cons_app(constant, constant)) -> c20(APP(constant, constant), ENCARG(constant)) ENCARG(cons_app(0, constant)) -> c20(APP(0, constant), ENCARG(0)) ENCARG(cons_app(+, constant)) -> c20(APP(+, constant), ENCARG(+)) ENCARG(cons_app(*, constant)) -> c20(APP(*, constant), ENCARG(*)) ENCARG(cons_app(-, constant)) -> c20(APP(-, constant), ENCARG(-)) ENCARG(cons_app(minus, constant)) -> c20(APP(minus, constant), ENCARG(minus)) ENCARG(cons_app(div, constant)) -> c20(APP(div, constant), ENCARG(div)) ENCARG(cons_app(pow, constant)) -> c20(APP(pow, constant), ENCARG(pow)) ENCARG(cons_app(2, constant)) -> c20(APP(2, constant), ENCARG(2)) ENCARG(cons_app(ln, constant)) -> c20(APP(ln, constant), ENCARG(ln)) ENCARG(cons_app(map, constant)) -> c20(APP(map, constant), ENCARG(map)) ENCARG(cons_app(nil, constant)) -> c20(APP(nil, constant), ENCARG(nil)) ENCARG(cons_app(cons, constant)) -> c20(APP(cons, constant), ENCARG(cons)) ENCARG(cons_app(filter, constant)) -> c20(APP(filter, constant), ENCARG(filter)) ENCARG(cons_app(filter2, constant)) -> c20(APP(filter2, constant), ENCARG(filter2)) ENCARG(cons_app(true, constant)) -> c20(APP(true, constant), ENCARG(true)) ENCARG(cons_app(false, constant)) -> c20(APP(false, constant), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 19 trailing nodes: ENCARG(cons_app(filter, constant)) -> c20(APP(filter, constant), ENCARG(filter)) ENCARG(cons_app(pow, constant)) -> c20(APP(pow, constant), ENCARG(pow)) ENCARG(cons_app(t, constant)) -> c20(APP(t, constant), ENCARG(t)) ENCARG(cons_app(cons, constant)) -> c20(APP(cons, constant), ENCARG(cons)) ENCARG(cons_app(false, constant)) -> c20(APP(false, constant), ENCARG(false)) ENCARG(cons_app(-, constant)) -> c20(APP(-, constant), ENCARG(-)) ENCARG(cons_app(+, constant)) -> c20(APP(+, constant), ENCARG(+)) ENCARG(cons_app(constant, constant)) -> c20(APP(constant, constant), ENCARG(constant)) ENCARG(cons_app(1, constant)) -> c20(APP(1, constant), ENCARG(1)) ENCARG(cons_app(map, constant)) -> c20(APP(map, constant), ENCARG(map)) ENCARG(cons_app(2, constant)) -> c20(APP(2, constant), ENCARG(2)) ENCARG(cons_app(ln, constant)) -> c20(APP(ln, constant), ENCARG(ln)) ENCARG(cons_app(filter2, constant)) -> c20(APP(filter2, constant), ENCARG(filter2)) ENCARG(cons_app(minus, constant)) -> c20(APP(minus, constant), ENCARG(minus)) ENCARG(cons_app(0, constant)) -> c20(APP(0, constant), ENCARG(0)) ENCARG(cons_app(div, constant)) -> c20(APP(div, constant), ENCARG(div)) ENCARG(cons_app(nil, constant)) -> c20(APP(nil, constant), ENCARG(nil)) ENCARG(cons_app(true, constant)) -> c20(APP(true, constant), ENCARG(true)) ENCARG(cons_app(*, constant)) -> c20(APP(*, constant), ENCARG(*)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(D)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c20(APP(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(D)) ENCARG(cons_app(t, 0)) -> c20(APP(t, 0), ENCARG(t)) ENCARG(cons_app(1, 0)) -> c20(APP(1, 0), ENCARG(1)) ENCARG(cons_app(constant, 0)) -> c20(APP(constant, 0), ENCARG(constant)) ENCARG(cons_app(0, 0)) -> c20(APP(0, 0), ENCARG(0)) ENCARG(cons_app(+, 0)) -> c20(APP(+, 0), ENCARG(+)) ENCARG(cons_app(*, 0)) -> c20(APP(*, 0), ENCARG(*)) ENCARG(cons_app(-, 0)) -> c20(APP(-, 0), ENCARG(-)) ENCARG(cons_app(minus, 0)) -> c20(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(div, 0)) -> c20(APP(div, 0), ENCARG(div)) ENCARG(cons_app(pow, 0)) -> c20(APP(pow, 0), ENCARG(pow)) ENCARG(cons_app(2, 0)) -> c20(APP(2, 0), ENCARG(2)) ENCARG(cons_app(ln, 0)) -> c20(APP(ln, 0), ENCARG(ln)) ENCARG(cons_app(map, 0)) -> c20(APP(map, 0), ENCARG(map)) ENCARG(cons_app(nil, 0)) -> c20(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c20(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c20(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c20(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(true, 0)) -> c20(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c20(APP(false, 0), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), 0)) -> c20(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(D)) ENCARG(cons_app(t, 0)) -> c20(APP(t, 0), ENCARG(t)) ENCARG(cons_app(1, 0)) -> c20(APP(1, 0), ENCARG(1)) ENCARG(cons_app(constant, 0)) -> c20(APP(constant, 0), ENCARG(constant)) ENCARG(cons_app(0, 0)) -> c20(APP(0, 0), ENCARG(0)) ENCARG(cons_app(+, 0)) -> c20(APP(+, 0), ENCARG(+)) ENCARG(cons_app(*, 0)) -> c20(APP(*, 0), ENCARG(*)) ENCARG(cons_app(-, 0)) -> c20(APP(-, 0), ENCARG(-)) ENCARG(cons_app(minus, 0)) -> c20(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(div, 0)) -> c20(APP(div, 0), ENCARG(div)) ENCARG(cons_app(pow, 0)) -> c20(APP(pow, 0), ENCARG(pow)) ENCARG(cons_app(2, 0)) -> c20(APP(2, 0), ENCARG(2)) ENCARG(cons_app(ln, 0)) -> c20(APP(ln, 0), ENCARG(ln)) ENCARG(cons_app(map, 0)) -> c20(APP(map, 0), ENCARG(map)) ENCARG(cons_app(nil, 0)) -> c20(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c20(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c20(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c20(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(true, 0)) -> c20(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c20(APP(false, 0), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(1, 0)) -> c20(APP(1, 0), ENCARG(1)) ENCARG(cons_app(filter, 0)) -> c20(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(minus, 0)) -> c20(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(+, 0)) -> c20(APP(+, 0), ENCARG(+)) ENCARG(cons_app(false, 0)) -> c20(APP(false, 0), ENCARG(false)) ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(D)) ENCARG(cons_app(div, 0)) -> c20(APP(div, 0), ENCARG(div)) ENCARG(cons_app(true, 0)) -> c20(APP(true, 0), ENCARG(true)) ENCARG(cons_app(filter2, 0)) -> c20(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(nil, 0)) -> c20(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(2, 0)) -> c20(APP(2, 0), ENCARG(2)) ENCARG(cons_app(pow, 0)) -> c20(APP(pow, 0), ENCARG(pow)) ENCARG(cons_app(0, 0)) -> c20(APP(0, 0), ENCARG(0)) ENCARG(cons_app(cons, 0)) -> c20(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(map, 0)) -> c20(APP(map, 0), ENCARG(map)) ENCARG(cons_app(t, 0)) -> c20(APP(t, 0), ENCARG(t)) ENCARG(cons_app(*, 0)) -> c20(APP(*, 0), ENCARG(*)) ENCARG(cons_app(ln, 0)) -> c20(APP(ln, 0), ENCARG(ln)) ENCARG(cons_app(-, 0)) -> c20(APP(-, 0), ENCARG(-)) ENCARG(cons_app(constant, 0)) -> c20(APP(constant, 0), ENCARG(constant)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, +)) -> c20(APP(encArg(x0), +), ENCARG(x0)) by ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(D)) ENCARG(cons_app(t, +)) -> c20(APP(t, +), ENCARG(t)) ENCARG(cons_app(1, +)) -> c20(APP(1, +), ENCARG(1)) ENCARG(cons_app(constant, +)) -> c20(APP(constant, +), ENCARG(constant)) ENCARG(cons_app(0, +)) -> c20(APP(0, +), ENCARG(0)) ENCARG(cons_app(+, +)) -> c20(APP(+, +), ENCARG(+)) ENCARG(cons_app(*, +)) -> c20(APP(*, +), ENCARG(*)) ENCARG(cons_app(-, +)) -> c20(APP(-, +), ENCARG(-)) ENCARG(cons_app(minus, +)) -> c20(APP(minus, +), ENCARG(minus)) ENCARG(cons_app(div, +)) -> c20(APP(div, +), ENCARG(div)) ENCARG(cons_app(pow, +)) -> c20(APP(pow, +), ENCARG(pow)) ENCARG(cons_app(2, +)) -> c20(APP(2, +), ENCARG(2)) ENCARG(cons_app(ln, +)) -> c20(APP(ln, +), ENCARG(ln)) ENCARG(cons_app(map, +)) -> c20(APP(map, +), ENCARG(map)) ENCARG(cons_app(nil, +)) -> c20(APP(nil, +), ENCARG(nil)) ENCARG(cons_app(cons, +)) -> c20(APP(cons, +), ENCARG(cons)) ENCARG(cons_app(filter, +)) -> c20(APP(filter, +), ENCARG(filter)) ENCARG(cons_app(filter2, +)) -> c20(APP(filter2, +), ENCARG(filter2)) ENCARG(cons_app(true, +)) -> c20(APP(true, +), ENCARG(true)) ENCARG(cons_app(false, +)) -> c20(APP(false, +), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), +)) -> c20(APP(app(encArg(z0), encArg(z1)), +), ENCARG(cons_app(z0, z1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(D)) ENCARG(cons_app(t, +)) -> c20(APP(t, +), ENCARG(t)) ENCARG(cons_app(1, +)) -> c20(APP(1, +), ENCARG(1)) ENCARG(cons_app(constant, +)) -> c20(APP(constant, +), ENCARG(constant)) ENCARG(cons_app(0, +)) -> c20(APP(0, +), ENCARG(0)) ENCARG(cons_app(+, +)) -> c20(APP(+, +), ENCARG(+)) ENCARG(cons_app(*, +)) -> c20(APP(*, +), ENCARG(*)) ENCARG(cons_app(-, +)) -> c20(APP(-, +), ENCARG(-)) ENCARG(cons_app(minus, +)) -> c20(APP(minus, +), ENCARG(minus)) ENCARG(cons_app(div, +)) -> c20(APP(div, +), ENCARG(div)) ENCARG(cons_app(pow, +)) -> c20(APP(pow, +), ENCARG(pow)) ENCARG(cons_app(2, +)) -> c20(APP(2, +), ENCARG(2)) ENCARG(cons_app(ln, +)) -> c20(APP(ln, +), ENCARG(ln)) ENCARG(cons_app(map, +)) -> c20(APP(map, +), ENCARG(map)) ENCARG(cons_app(nil, +)) -> c20(APP(nil, +), ENCARG(nil)) ENCARG(cons_app(cons, +)) -> c20(APP(cons, +), ENCARG(cons)) ENCARG(cons_app(filter, +)) -> c20(APP(filter, +), ENCARG(filter)) ENCARG(cons_app(filter2, +)) -> c20(APP(filter2, +), ENCARG(filter2)) ENCARG(cons_app(true, +)) -> c20(APP(true, +), ENCARG(true)) ENCARG(cons_app(false, +)) -> c20(APP(false, +), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(nil, +)) -> c20(APP(nil, +), ENCARG(nil)) ENCARG(cons_app(-, +)) -> c20(APP(-, +), ENCARG(-)) ENCARG(cons_app(constant, +)) -> c20(APP(constant, +), ENCARG(constant)) ENCARG(cons_app(t, +)) -> c20(APP(t, +), ENCARG(t)) ENCARG(cons_app(2, +)) -> c20(APP(2, +), ENCARG(2)) ENCARG(cons_app(false, +)) -> c20(APP(false, +), ENCARG(false)) ENCARG(cons_app(map, +)) -> c20(APP(map, +), ENCARG(map)) ENCARG(cons_app(*, +)) -> c20(APP(*, +), ENCARG(*)) ENCARG(cons_app(pow, +)) -> c20(APP(pow, +), ENCARG(pow)) ENCARG(cons_app(ln, +)) -> c20(APP(ln, +), ENCARG(ln)) ENCARG(cons_app(div, +)) -> c20(APP(div, +), ENCARG(div)) ENCARG(cons_app(minus, +)) -> c20(APP(minus, +), ENCARG(minus)) ENCARG(cons_app(true, +)) -> c20(APP(true, +), ENCARG(true)) ENCARG(cons_app(+, +)) -> c20(APP(+, +), ENCARG(+)) ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(D)) ENCARG(cons_app(cons, +)) -> c20(APP(cons, +), ENCARG(cons)) ENCARG(cons_app(filter2, +)) -> c20(APP(filter2, +), ENCARG(filter2)) ENCARG(cons_app(0, +)) -> c20(APP(0, +), ENCARG(0)) ENCARG(cons_app(filter, +)) -> c20(APP(filter, +), ENCARG(filter)) ENCARG(cons_app(1, +)) -> c20(APP(1, +), ENCARG(1)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, *)) -> c20(APP(encArg(x0), *), ENCARG(x0)) by ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(D)) ENCARG(cons_app(t, *)) -> c20(APP(t, *), ENCARG(t)) ENCARG(cons_app(1, *)) -> c20(APP(1, *), ENCARG(1)) ENCARG(cons_app(constant, *)) -> c20(APP(constant, *), ENCARG(constant)) ENCARG(cons_app(0, *)) -> c20(APP(0, *), ENCARG(0)) ENCARG(cons_app(+, *)) -> c20(APP(+, *), ENCARG(+)) ENCARG(cons_app(*, *)) -> c20(APP(*, *), ENCARG(*)) ENCARG(cons_app(-, *)) -> c20(APP(-, *), ENCARG(-)) ENCARG(cons_app(minus, *)) -> c20(APP(minus, *), ENCARG(minus)) ENCARG(cons_app(div, *)) -> c20(APP(div, *), ENCARG(div)) ENCARG(cons_app(pow, *)) -> c20(APP(pow, *), ENCARG(pow)) ENCARG(cons_app(2, *)) -> c20(APP(2, *), ENCARG(2)) ENCARG(cons_app(ln, *)) -> c20(APP(ln, *), ENCARG(ln)) ENCARG(cons_app(map, *)) -> c20(APP(map, *), ENCARG(map)) ENCARG(cons_app(nil, *)) -> c20(APP(nil, *), ENCARG(nil)) ENCARG(cons_app(cons, *)) -> c20(APP(cons, *), ENCARG(cons)) ENCARG(cons_app(filter, *)) -> c20(APP(filter, *), ENCARG(filter)) ENCARG(cons_app(filter2, *)) -> c20(APP(filter2, *), ENCARG(filter2)) ENCARG(cons_app(true, *)) -> c20(APP(true, *), ENCARG(true)) ENCARG(cons_app(false, *)) -> c20(APP(false, *), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), *)) -> c20(APP(app(encArg(z0), encArg(z1)), *), ENCARG(cons_app(z0, z1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(D)) ENCARG(cons_app(t, *)) -> c20(APP(t, *), ENCARG(t)) ENCARG(cons_app(1, *)) -> c20(APP(1, *), ENCARG(1)) ENCARG(cons_app(constant, *)) -> c20(APP(constant, *), ENCARG(constant)) ENCARG(cons_app(0, *)) -> c20(APP(0, *), ENCARG(0)) ENCARG(cons_app(+, *)) -> c20(APP(+, *), ENCARG(+)) ENCARG(cons_app(*, *)) -> c20(APP(*, *), ENCARG(*)) ENCARG(cons_app(-, *)) -> c20(APP(-, *), ENCARG(-)) ENCARG(cons_app(minus, *)) -> c20(APP(minus, *), ENCARG(minus)) ENCARG(cons_app(div, *)) -> c20(APP(div, *), ENCARG(div)) ENCARG(cons_app(pow, *)) -> c20(APP(pow, *), ENCARG(pow)) ENCARG(cons_app(2, *)) -> c20(APP(2, *), ENCARG(2)) ENCARG(cons_app(ln, *)) -> c20(APP(ln, *), ENCARG(ln)) ENCARG(cons_app(map, *)) -> c20(APP(map, *), ENCARG(map)) ENCARG(cons_app(nil, *)) -> c20(APP(nil, *), ENCARG(nil)) ENCARG(cons_app(cons, *)) -> c20(APP(cons, *), ENCARG(cons)) ENCARG(cons_app(filter, *)) -> c20(APP(filter, *), ENCARG(filter)) ENCARG(cons_app(filter2, *)) -> c20(APP(filter2, *), ENCARG(filter2)) ENCARG(cons_app(true, *)) -> c20(APP(true, *), ENCARG(true)) ENCARG(cons_app(false, *)) -> c20(APP(false, *), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(2, *)) -> c20(APP(2, *), ENCARG(2)) ENCARG(cons_app(+, *)) -> c20(APP(+, *), ENCARG(+)) ENCARG(cons_app(filter2, *)) -> c20(APP(filter2, *), ENCARG(filter2)) ENCARG(cons_app(filter, *)) -> c20(APP(filter, *), ENCARG(filter)) ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(D)) ENCARG(cons_app(ln, *)) -> c20(APP(ln, *), ENCARG(ln)) ENCARG(cons_app(-, *)) -> c20(APP(-, *), ENCARG(-)) ENCARG(cons_app(constant, *)) -> c20(APP(constant, *), ENCARG(constant)) ENCARG(cons_app(div, *)) -> c20(APP(div, *), ENCARG(div)) ENCARG(cons_app(1, *)) -> c20(APP(1, *), ENCARG(1)) ENCARG(cons_app(true, *)) -> c20(APP(true, *), ENCARG(true)) ENCARG(cons_app(t, *)) -> c20(APP(t, *), ENCARG(t)) ENCARG(cons_app(cons, *)) -> c20(APP(cons, *), ENCARG(cons)) ENCARG(cons_app(*, *)) -> c20(APP(*, *), ENCARG(*)) ENCARG(cons_app(false, *)) -> c20(APP(false, *), ENCARG(false)) ENCARG(cons_app(pow, *)) -> c20(APP(pow, *), ENCARG(pow)) ENCARG(cons_app(0, *)) -> c20(APP(0, *), ENCARG(0)) ENCARG(cons_app(nil, *)) -> c20(APP(nil, *), ENCARG(nil)) ENCARG(cons_app(minus, *)) -> c20(APP(minus, *), ENCARG(minus)) ENCARG(cons_app(map, *)) -> c20(APP(map, *), ENCARG(map)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, -)) -> c20(APP(encArg(x0), -), ENCARG(x0)) by ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(D)) ENCARG(cons_app(t, -)) -> c20(APP(t, -), ENCARG(t)) ENCARG(cons_app(1, -)) -> c20(APP(1, -), ENCARG(1)) ENCARG(cons_app(constant, -)) -> c20(APP(constant, -), ENCARG(constant)) ENCARG(cons_app(0, -)) -> c20(APP(0, -), ENCARG(0)) ENCARG(cons_app(+, -)) -> c20(APP(+, -), ENCARG(+)) ENCARG(cons_app(*, -)) -> c20(APP(*, -), ENCARG(*)) ENCARG(cons_app(-, -)) -> c20(APP(-, -), ENCARG(-)) ENCARG(cons_app(minus, -)) -> c20(APP(minus, -), ENCARG(minus)) ENCARG(cons_app(div, -)) -> c20(APP(div, -), ENCARG(div)) ENCARG(cons_app(pow, -)) -> c20(APP(pow, -), ENCARG(pow)) ENCARG(cons_app(2, -)) -> c20(APP(2, -), ENCARG(2)) ENCARG(cons_app(ln, -)) -> c20(APP(ln, -), ENCARG(ln)) ENCARG(cons_app(map, -)) -> c20(APP(map, -), ENCARG(map)) ENCARG(cons_app(nil, -)) -> c20(APP(nil, -), ENCARG(nil)) ENCARG(cons_app(cons, -)) -> c20(APP(cons, -), ENCARG(cons)) ENCARG(cons_app(filter, -)) -> c20(APP(filter, -), ENCARG(filter)) ENCARG(cons_app(filter2, -)) -> c20(APP(filter2, -), ENCARG(filter2)) ENCARG(cons_app(true, -)) -> c20(APP(true, -), ENCARG(true)) ENCARG(cons_app(false, -)) -> c20(APP(false, -), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), -)) -> c20(APP(app(encArg(z0), encArg(z1)), -), ENCARG(cons_app(z0, z1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(D)) ENCARG(cons_app(t, -)) -> c20(APP(t, -), ENCARG(t)) ENCARG(cons_app(1, -)) -> c20(APP(1, -), ENCARG(1)) ENCARG(cons_app(constant, -)) -> c20(APP(constant, -), ENCARG(constant)) ENCARG(cons_app(0, -)) -> c20(APP(0, -), ENCARG(0)) ENCARG(cons_app(+, -)) -> c20(APP(+, -), ENCARG(+)) ENCARG(cons_app(*, -)) -> c20(APP(*, -), ENCARG(*)) ENCARG(cons_app(-, -)) -> c20(APP(-, -), ENCARG(-)) ENCARG(cons_app(minus, -)) -> c20(APP(minus, -), ENCARG(minus)) ENCARG(cons_app(div, -)) -> c20(APP(div, -), ENCARG(div)) ENCARG(cons_app(pow, -)) -> c20(APP(pow, -), ENCARG(pow)) ENCARG(cons_app(2, -)) -> c20(APP(2, -), ENCARG(2)) ENCARG(cons_app(ln, -)) -> c20(APP(ln, -), ENCARG(ln)) ENCARG(cons_app(map, -)) -> c20(APP(map, -), ENCARG(map)) ENCARG(cons_app(nil, -)) -> c20(APP(nil, -), ENCARG(nil)) ENCARG(cons_app(cons, -)) -> c20(APP(cons, -), ENCARG(cons)) ENCARG(cons_app(filter, -)) -> c20(APP(filter, -), ENCARG(filter)) ENCARG(cons_app(filter2, -)) -> c20(APP(filter2, -), ENCARG(filter2)) ENCARG(cons_app(true, -)) -> c20(APP(true, -), ENCARG(true)) ENCARG(cons_app(false, -)) -> c20(APP(false, -), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(div, -)) -> c20(APP(div, -), ENCARG(div)) ENCARG(cons_app(nil, -)) -> c20(APP(nil, -), ENCARG(nil)) ENCARG(cons_app(*, -)) -> c20(APP(*, -), ENCARG(*)) ENCARG(cons_app(+, -)) -> c20(APP(+, -), ENCARG(+)) ENCARG(cons_app(ln, -)) -> c20(APP(ln, -), ENCARG(ln)) ENCARG(cons_app(minus, -)) -> c20(APP(minus, -), ENCARG(minus)) ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(D)) ENCARG(cons_app(true, -)) -> c20(APP(true, -), ENCARG(true)) ENCARG(cons_app(filter2, -)) -> c20(APP(filter2, -), ENCARG(filter2)) ENCARG(cons_app(1, -)) -> c20(APP(1, -), ENCARG(1)) ENCARG(cons_app(pow, -)) -> c20(APP(pow, -), ENCARG(pow)) ENCARG(cons_app(cons, -)) -> c20(APP(cons, -), ENCARG(cons)) ENCARG(cons_app(2, -)) -> c20(APP(2, -), ENCARG(2)) ENCARG(cons_app(false, -)) -> c20(APP(false, -), ENCARG(false)) ENCARG(cons_app(filter, -)) -> c20(APP(filter, -), ENCARG(filter)) ENCARG(cons_app(0, -)) -> c20(APP(0, -), ENCARG(0)) ENCARG(cons_app(t, -)) -> c20(APP(t, -), ENCARG(t)) ENCARG(cons_app(-, -)) -> c20(APP(-, -), ENCARG(-)) ENCARG(cons_app(constant, -)) -> c20(APP(constant, -), ENCARG(constant)) ENCARG(cons_app(map, -)) -> c20(APP(map, -), ENCARG(map)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, minus)) -> c20(APP(encArg(x0), minus), ENCARG(x0)) by ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(D)) ENCARG(cons_app(t, minus)) -> c20(APP(t, minus), ENCARG(t)) ENCARG(cons_app(1, minus)) -> c20(APP(1, minus), ENCARG(1)) ENCARG(cons_app(constant, minus)) -> c20(APP(constant, minus), ENCARG(constant)) ENCARG(cons_app(0, minus)) -> c20(APP(0, minus), ENCARG(0)) ENCARG(cons_app(+, minus)) -> c20(APP(+, minus), ENCARG(+)) ENCARG(cons_app(*, minus)) -> c20(APP(*, minus), ENCARG(*)) ENCARG(cons_app(-, minus)) -> c20(APP(-, minus), ENCARG(-)) ENCARG(cons_app(minus, minus)) -> c20(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(div, minus)) -> c20(APP(div, minus), ENCARG(div)) ENCARG(cons_app(pow, minus)) -> c20(APP(pow, minus), ENCARG(pow)) ENCARG(cons_app(2, minus)) -> c20(APP(2, minus), ENCARG(2)) ENCARG(cons_app(ln, minus)) -> c20(APP(ln, minus), ENCARG(ln)) ENCARG(cons_app(map, minus)) -> c20(APP(map, minus), ENCARG(map)) ENCARG(cons_app(nil, minus)) -> c20(APP(nil, minus), ENCARG(nil)) ENCARG(cons_app(cons, minus)) -> c20(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(filter, minus)) -> c20(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(filter2, minus)) -> c20(APP(filter2, minus), ENCARG(filter2)) ENCARG(cons_app(true, minus)) -> c20(APP(true, minus), ENCARG(true)) ENCARG(cons_app(false, minus)) -> c20(APP(false, minus), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), minus)) -> c20(APP(app(encArg(z0), encArg(z1)), minus), ENCARG(cons_app(z0, z1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(D)) ENCARG(cons_app(t, minus)) -> c20(APP(t, minus), ENCARG(t)) ENCARG(cons_app(1, minus)) -> c20(APP(1, minus), ENCARG(1)) ENCARG(cons_app(constant, minus)) -> c20(APP(constant, minus), ENCARG(constant)) ENCARG(cons_app(0, minus)) -> c20(APP(0, minus), ENCARG(0)) ENCARG(cons_app(+, minus)) -> c20(APP(+, minus), ENCARG(+)) ENCARG(cons_app(*, minus)) -> c20(APP(*, minus), ENCARG(*)) ENCARG(cons_app(-, minus)) -> c20(APP(-, minus), ENCARG(-)) ENCARG(cons_app(minus, minus)) -> c20(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(div, minus)) -> c20(APP(div, minus), ENCARG(div)) ENCARG(cons_app(pow, minus)) -> c20(APP(pow, minus), ENCARG(pow)) ENCARG(cons_app(2, minus)) -> c20(APP(2, minus), ENCARG(2)) ENCARG(cons_app(ln, minus)) -> c20(APP(ln, minus), ENCARG(ln)) ENCARG(cons_app(map, minus)) -> c20(APP(map, minus), ENCARG(map)) ENCARG(cons_app(nil, minus)) -> c20(APP(nil, minus), ENCARG(nil)) ENCARG(cons_app(cons, minus)) -> c20(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(filter, minus)) -> c20(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(filter2, minus)) -> c20(APP(filter2, minus), ENCARG(filter2)) ENCARG(cons_app(true, minus)) -> c20(APP(true, minus), ENCARG(true)) ENCARG(cons_app(false, minus)) -> c20(APP(false, minus), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(-, minus)) -> c20(APP(-, minus), ENCARG(-)) ENCARG(cons_app(constant, minus)) -> c20(APP(constant, minus), ENCARG(constant)) ENCARG(cons_app(t, minus)) -> c20(APP(t, minus), ENCARG(t)) ENCARG(cons_app(*, minus)) -> c20(APP(*, minus), ENCARG(*)) ENCARG(cons_app(filter, minus)) -> c20(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(ln, minus)) -> c20(APP(ln, minus), ENCARG(ln)) ENCARG(cons_app(minus, minus)) -> c20(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(pow, minus)) -> c20(APP(pow, minus), ENCARG(pow)) ENCARG(cons_app(true, minus)) -> c20(APP(true, minus), ENCARG(true)) ENCARG(cons_app(2, minus)) -> c20(APP(2, minus), ENCARG(2)) ENCARG(cons_app(filter2, minus)) -> c20(APP(filter2, minus), ENCARG(filter2)) ENCARG(cons_app(cons, minus)) -> c20(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(map, minus)) -> c20(APP(map, minus), ENCARG(map)) ENCARG(cons_app(div, minus)) -> c20(APP(div, minus), ENCARG(div)) ENCARG(cons_app(+, minus)) -> c20(APP(+, minus), ENCARG(+)) ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(D)) ENCARG(cons_app(nil, minus)) -> c20(APP(nil, minus), ENCARG(nil)) ENCARG(cons_app(false, minus)) -> c20(APP(false, minus), ENCARG(false)) ENCARG(cons_app(1, minus)) -> c20(APP(1, minus), ENCARG(1)) ENCARG(cons_app(0, minus)) -> c20(APP(0, minus), ENCARG(0)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, div)) -> c20(APP(encArg(x0), div), ENCARG(x0)) by ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(D)) ENCARG(cons_app(t, div)) -> c20(APP(t, div), ENCARG(t)) ENCARG(cons_app(1, div)) -> c20(APP(1, div), ENCARG(1)) ENCARG(cons_app(constant, div)) -> c20(APP(constant, div), ENCARG(constant)) ENCARG(cons_app(0, div)) -> c20(APP(0, div), ENCARG(0)) ENCARG(cons_app(+, div)) -> c20(APP(+, div), ENCARG(+)) ENCARG(cons_app(*, div)) -> c20(APP(*, div), ENCARG(*)) ENCARG(cons_app(-, div)) -> c20(APP(-, div), ENCARG(-)) ENCARG(cons_app(minus, div)) -> c20(APP(minus, div), ENCARG(minus)) ENCARG(cons_app(div, div)) -> c20(APP(div, div), ENCARG(div)) ENCARG(cons_app(pow, div)) -> c20(APP(pow, div), ENCARG(pow)) ENCARG(cons_app(2, div)) -> c20(APP(2, div), ENCARG(2)) ENCARG(cons_app(ln, div)) -> c20(APP(ln, div), ENCARG(ln)) ENCARG(cons_app(map, div)) -> c20(APP(map, div), ENCARG(map)) ENCARG(cons_app(nil, div)) -> c20(APP(nil, div), ENCARG(nil)) ENCARG(cons_app(cons, div)) -> c20(APP(cons, div), ENCARG(cons)) ENCARG(cons_app(filter, div)) -> c20(APP(filter, div), ENCARG(filter)) ENCARG(cons_app(filter2, div)) -> c20(APP(filter2, div), ENCARG(filter2)) ENCARG(cons_app(true, div)) -> c20(APP(true, div), ENCARG(true)) ENCARG(cons_app(false, div)) -> c20(APP(false, div), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), div)) -> c20(APP(app(encArg(z0), encArg(z1)), div), ENCARG(cons_app(z0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(D)) ENCARG(cons_app(t, div)) -> c20(APP(t, div), ENCARG(t)) ENCARG(cons_app(1, div)) -> c20(APP(1, div), ENCARG(1)) ENCARG(cons_app(constant, div)) -> c20(APP(constant, div), ENCARG(constant)) ENCARG(cons_app(0, div)) -> c20(APP(0, div), ENCARG(0)) ENCARG(cons_app(+, div)) -> c20(APP(+, div), ENCARG(+)) ENCARG(cons_app(*, div)) -> c20(APP(*, div), ENCARG(*)) ENCARG(cons_app(-, div)) -> c20(APP(-, div), ENCARG(-)) ENCARG(cons_app(minus, div)) -> c20(APP(minus, div), ENCARG(minus)) ENCARG(cons_app(div, div)) -> c20(APP(div, div), ENCARG(div)) ENCARG(cons_app(pow, div)) -> c20(APP(pow, div), ENCARG(pow)) ENCARG(cons_app(2, div)) -> c20(APP(2, div), ENCARG(2)) ENCARG(cons_app(ln, div)) -> c20(APP(ln, div), ENCARG(ln)) ENCARG(cons_app(map, div)) -> c20(APP(map, div), ENCARG(map)) ENCARG(cons_app(nil, div)) -> c20(APP(nil, div), ENCARG(nil)) ENCARG(cons_app(cons, div)) -> c20(APP(cons, div), ENCARG(cons)) ENCARG(cons_app(filter, div)) -> c20(APP(filter, div), ENCARG(filter)) ENCARG(cons_app(filter2, div)) -> c20(APP(filter2, div), ENCARG(filter2)) ENCARG(cons_app(true, div)) -> c20(APP(true, div), ENCARG(true)) ENCARG(cons_app(false, div)) -> c20(APP(false, div), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(minus, div)) -> c20(APP(minus, div), ENCARG(minus)) ENCARG(cons_app(map, div)) -> c20(APP(map, div), ENCARG(map)) ENCARG(cons_app(2, div)) -> c20(APP(2, div), ENCARG(2)) ENCARG(cons_app(+, div)) -> c20(APP(+, div), ENCARG(+)) ENCARG(cons_app(cons, div)) -> c20(APP(cons, div), ENCARG(cons)) ENCARG(cons_app(true, div)) -> c20(APP(true, div), ENCARG(true)) ENCARG(cons_app(filter2, div)) -> c20(APP(filter2, div), ENCARG(filter2)) ENCARG(cons_app(*, div)) -> c20(APP(*, div), ENCARG(*)) ENCARG(cons_app(0, div)) -> c20(APP(0, div), ENCARG(0)) ENCARG(cons_app(1, div)) -> c20(APP(1, div), ENCARG(1)) ENCARG(cons_app(-, div)) -> c20(APP(-, div), ENCARG(-)) ENCARG(cons_app(constant, div)) -> c20(APP(constant, div), ENCARG(constant)) ENCARG(cons_app(false, div)) -> c20(APP(false, div), ENCARG(false)) ENCARG(cons_app(t, div)) -> c20(APP(t, div), ENCARG(t)) ENCARG(cons_app(nil, div)) -> c20(APP(nil, div), ENCARG(nil)) ENCARG(cons_app(div, div)) -> c20(APP(div, div), ENCARG(div)) ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(D)) ENCARG(cons_app(pow, div)) -> c20(APP(pow, div), ENCARG(pow)) ENCARG(cons_app(filter, div)) -> c20(APP(filter, div), ENCARG(filter)) ENCARG(cons_app(ln, div)) -> c20(APP(ln, div), ENCARG(ln)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, pow)) -> c20(APP(encArg(x0), pow), ENCARG(x0)) by ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(D)) ENCARG(cons_app(t, pow)) -> c20(APP(t, pow), ENCARG(t)) ENCARG(cons_app(1, pow)) -> c20(APP(1, pow), ENCARG(1)) ENCARG(cons_app(constant, pow)) -> c20(APP(constant, pow), ENCARG(constant)) ENCARG(cons_app(0, pow)) -> c20(APP(0, pow), ENCARG(0)) ENCARG(cons_app(+, pow)) -> c20(APP(+, pow), ENCARG(+)) ENCARG(cons_app(*, pow)) -> c20(APP(*, pow), ENCARG(*)) ENCARG(cons_app(-, pow)) -> c20(APP(-, pow), ENCARG(-)) ENCARG(cons_app(minus, pow)) -> c20(APP(minus, pow), ENCARG(minus)) ENCARG(cons_app(div, pow)) -> c20(APP(div, pow), ENCARG(div)) ENCARG(cons_app(pow, pow)) -> c20(APP(pow, pow), ENCARG(pow)) ENCARG(cons_app(2, pow)) -> c20(APP(2, pow), ENCARG(2)) ENCARG(cons_app(ln, pow)) -> c20(APP(ln, pow), ENCARG(ln)) ENCARG(cons_app(map, pow)) -> c20(APP(map, pow), ENCARG(map)) ENCARG(cons_app(nil, pow)) -> c20(APP(nil, pow), ENCARG(nil)) ENCARG(cons_app(cons, pow)) -> c20(APP(cons, pow), ENCARG(cons)) ENCARG(cons_app(filter, pow)) -> c20(APP(filter, pow), ENCARG(filter)) ENCARG(cons_app(filter2, pow)) -> c20(APP(filter2, pow), ENCARG(filter2)) ENCARG(cons_app(true, pow)) -> c20(APP(true, pow), ENCARG(true)) ENCARG(cons_app(false, pow)) -> c20(APP(false, pow), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), pow)) -> c20(APP(app(encArg(z0), encArg(z1)), pow), ENCARG(cons_app(z0, z1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(D)) ENCARG(cons_app(t, pow)) -> c20(APP(t, pow), ENCARG(t)) ENCARG(cons_app(1, pow)) -> c20(APP(1, pow), ENCARG(1)) ENCARG(cons_app(constant, pow)) -> c20(APP(constant, pow), ENCARG(constant)) ENCARG(cons_app(0, pow)) -> c20(APP(0, pow), ENCARG(0)) ENCARG(cons_app(+, pow)) -> c20(APP(+, pow), ENCARG(+)) ENCARG(cons_app(*, pow)) -> c20(APP(*, pow), ENCARG(*)) ENCARG(cons_app(-, pow)) -> c20(APP(-, pow), ENCARG(-)) ENCARG(cons_app(minus, pow)) -> c20(APP(minus, pow), ENCARG(minus)) ENCARG(cons_app(div, pow)) -> c20(APP(div, pow), ENCARG(div)) ENCARG(cons_app(pow, pow)) -> c20(APP(pow, pow), ENCARG(pow)) ENCARG(cons_app(2, pow)) -> c20(APP(2, pow), ENCARG(2)) ENCARG(cons_app(ln, pow)) -> c20(APP(ln, pow), ENCARG(ln)) ENCARG(cons_app(map, pow)) -> c20(APP(map, pow), ENCARG(map)) ENCARG(cons_app(nil, pow)) -> c20(APP(nil, pow), ENCARG(nil)) ENCARG(cons_app(cons, pow)) -> c20(APP(cons, pow), ENCARG(cons)) ENCARG(cons_app(filter, pow)) -> c20(APP(filter, pow), ENCARG(filter)) ENCARG(cons_app(filter2, pow)) -> c20(APP(filter2, pow), ENCARG(filter2)) ENCARG(cons_app(true, pow)) -> c20(APP(true, pow), ENCARG(true)) ENCARG(cons_app(false, pow)) -> c20(APP(false, pow), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(filter, pow)) -> c20(APP(filter, pow), ENCARG(filter)) ENCARG(cons_app(ln, pow)) -> c20(APP(ln, pow), ENCARG(ln)) ENCARG(cons_app(1, pow)) -> c20(APP(1, pow), ENCARG(1)) ENCARG(cons_app(pow, pow)) -> c20(APP(pow, pow), ENCARG(pow)) ENCARG(cons_app(+, pow)) -> c20(APP(+, pow), ENCARG(+)) ENCARG(cons_app(cons, pow)) -> c20(APP(cons, pow), ENCARG(cons)) ENCARG(cons_app(-, pow)) -> c20(APP(-, pow), ENCARG(-)) ENCARG(cons_app(constant, pow)) -> c20(APP(constant, pow), ENCARG(constant)) ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(D)) ENCARG(cons_app(map, pow)) -> c20(APP(map, pow), ENCARG(map)) ENCARG(cons_app(div, pow)) -> c20(APP(div, pow), ENCARG(div)) ENCARG(cons_app(t, pow)) -> c20(APP(t, pow), ENCARG(t)) ENCARG(cons_app(2, pow)) -> c20(APP(2, pow), ENCARG(2)) ENCARG(cons_app(filter2, pow)) -> c20(APP(filter2, pow), ENCARG(filter2)) ENCARG(cons_app(true, pow)) -> c20(APP(true, pow), ENCARG(true)) ENCARG(cons_app(nil, pow)) -> c20(APP(nil, pow), ENCARG(nil)) ENCARG(cons_app(minus, pow)) -> c20(APP(minus, pow), ENCARG(minus)) ENCARG(cons_app(false, pow)) -> c20(APP(false, pow), ENCARG(false)) ENCARG(cons_app(0, pow)) -> c20(APP(0, pow), ENCARG(0)) ENCARG(cons_app(*, pow)) -> c20(APP(*, pow), ENCARG(*)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 2)) -> c20(APP(encArg(x0), 2), ENCARG(x0)) by ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(D)) ENCARG(cons_app(t, 2)) -> c20(APP(t, 2), ENCARG(t)) ENCARG(cons_app(1, 2)) -> c20(APP(1, 2), ENCARG(1)) ENCARG(cons_app(constant, 2)) -> c20(APP(constant, 2), ENCARG(constant)) ENCARG(cons_app(0, 2)) -> c20(APP(0, 2), ENCARG(0)) ENCARG(cons_app(+, 2)) -> c20(APP(+, 2), ENCARG(+)) ENCARG(cons_app(*, 2)) -> c20(APP(*, 2), ENCARG(*)) ENCARG(cons_app(-, 2)) -> c20(APP(-, 2), ENCARG(-)) ENCARG(cons_app(minus, 2)) -> c20(APP(minus, 2), ENCARG(minus)) ENCARG(cons_app(div, 2)) -> c20(APP(div, 2), ENCARG(div)) ENCARG(cons_app(pow, 2)) -> c20(APP(pow, 2), ENCARG(pow)) ENCARG(cons_app(2, 2)) -> c20(APP(2, 2), ENCARG(2)) ENCARG(cons_app(ln, 2)) -> c20(APP(ln, 2), ENCARG(ln)) ENCARG(cons_app(map, 2)) -> c20(APP(map, 2), ENCARG(map)) ENCARG(cons_app(nil, 2)) -> c20(APP(nil, 2), ENCARG(nil)) ENCARG(cons_app(cons, 2)) -> c20(APP(cons, 2), ENCARG(cons)) ENCARG(cons_app(filter, 2)) -> c20(APP(filter, 2), ENCARG(filter)) ENCARG(cons_app(filter2, 2)) -> c20(APP(filter2, 2), ENCARG(filter2)) ENCARG(cons_app(true, 2)) -> c20(APP(true, 2), ENCARG(true)) ENCARG(cons_app(false, 2)) -> c20(APP(false, 2), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), 2)) -> c20(APP(app(encArg(z0), encArg(z1)), 2), ENCARG(cons_app(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(D)) ENCARG(cons_app(t, 2)) -> c20(APP(t, 2), ENCARG(t)) ENCARG(cons_app(1, 2)) -> c20(APP(1, 2), ENCARG(1)) ENCARG(cons_app(constant, 2)) -> c20(APP(constant, 2), ENCARG(constant)) ENCARG(cons_app(0, 2)) -> c20(APP(0, 2), ENCARG(0)) ENCARG(cons_app(+, 2)) -> c20(APP(+, 2), ENCARG(+)) ENCARG(cons_app(*, 2)) -> c20(APP(*, 2), ENCARG(*)) ENCARG(cons_app(-, 2)) -> c20(APP(-, 2), ENCARG(-)) ENCARG(cons_app(minus, 2)) -> c20(APP(minus, 2), ENCARG(minus)) ENCARG(cons_app(div, 2)) -> c20(APP(div, 2), ENCARG(div)) ENCARG(cons_app(pow, 2)) -> c20(APP(pow, 2), ENCARG(pow)) ENCARG(cons_app(2, 2)) -> c20(APP(2, 2), ENCARG(2)) ENCARG(cons_app(ln, 2)) -> c20(APP(ln, 2), ENCARG(ln)) ENCARG(cons_app(map, 2)) -> c20(APP(map, 2), ENCARG(map)) ENCARG(cons_app(nil, 2)) -> c20(APP(nil, 2), ENCARG(nil)) ENCARG(cons_app(cons, 2)) -> c20(APP(cons, 2), ENCARG(cons)) ENCARG(cons_app(filter, 2)) -> c20(APP(filter, 2), ENCARG(filter)) ENCARG(cons_app(filter2, 2)) -> c20(APP(filter2, 2), ENCARG(filter2)) ENCARG(cons_app(true, 2)) -> c20(APP(true, 2), ENCARG(true)) ENCARG(cons_app(false, 2)) -> c20(APP(false, 2), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(*, 2)) -> c20(APP(*, 2), ENCARG(*)) ENCARG(cons_app(pow, 2)) -> c20(APP(pow, 2), ENCARG(pow)) ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(D)) ENCARG(cons_app(nil, 2)) -> c20(APP(nil, 2), ENCARG(nil)) ENCARG(cons_app(ln, 2)) -> c20(APP(ln, 2), ENCARG(ln)) ENCARG(cons_app(+, 2)) -> c20(APP(+, 2), ENCARG(+)) ENCARG(cons_app(0, 2)) -> c20(APP(0, 2), ENCARG(0)) ENCARG(cons_app(cons, 2)) -> c20(APP(cons, 2), ENCARG(cons)) ENCARG(cons_app(1, 2)) -> c20(APP(1, 2), ENCARG(1)) ENCARG(cons_app(filter, 2)) -> c20(APP(filter, 2), ENCARG(filter)) ENCARG(cons_app(2, 2)) -> c20(APP(2, 2), ENCARG(2)) ENCARG(cons_app(-, 2)) -> c20(APP(-, 2), ENCARG(-)) ENCARG(cons_app(constant, 2)) -> c20(APP(constant, 2), ENCARG(constant)) ENCARG(cons_app(t, 2)) -> c20(APP(t, 2), ENCARG(t)) ENCARG(cons_app(true, 2)) -> c20(APP(true, 2), ENCARG(true)) ENCARG(cons_app(false, 2)) -> c20(APP(false, 2), ENCARG(false)) ENCARG(cons_app(div, 2)) -> c20(APP(div, 2), ENCARG(div)) ENCARG(cons_app(filter2, 2)) -> c20(APP(filter2, 2), ENCARG(filter2)) ENCARG(cons_app(map, 2)) -> c20(APP(map, 2), ENCARG(map)) ENCARG(cons_app(minus, 2)) -> c20(APP(minus, 2), ENCARG(minus)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, ln)) -> c20(APP(encArg(x0), ln), ENCARG(x0)) by ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(D)) ENCARG(cons_app(t, ln)) -> c20(APP(t, ln), ENCARG(t)) ENCARG(cons_app(1, ln)) -> c20(APP(1, ln), ENCARG(1)) ENCARG(cons_app(constant, ln)) -> c20(APP(constant, ln), ENCARG(constant)) ENCARG(cons_app(0, ln)) -> c20(APP(0, ln), ENCARG(0)) ENCARG(cons_app(+, ln)) -> c20(APP(+, ln), ENCARG(+)) ENCARG(cons_app(*, ln)) -> c20(APP(*, ln), ENCARG(*)) ENCARG(cons_app(-, ln)) -> c20(APP(-, ln), ENCARG(-)) ENCARG(cons_app(minus, ln)) -> c20(APP(minus, ln), ENCARG(minus)) ENCARG(cons_app(div, ln)) -> c20(APP(div, ln), ENCARG(div)) ENCARG(cons_app(pow, ln)) -> c20(APP(pow, ln), ENCARG(pow)) ENCARG(cons_app(2, ln)) -> c20(APP(2, ln), ENCARG(2)) ENCARG(cons_app(ln, ln)) -> c20(APP(ln, ln), ENCARG(ln)) ENCARG(cons_app(map, ln)) -> c20(APP(map, ln), ENCARG(map)) ENCARG(cons_app(nil, ln)) -> c20(APP(nil, ln), ENCARG(nil)) ENCARG(cons_app(cons, ln)) -> c20(APP(cons, ln), ENCARG(cons)) ENCARG(cons_app(filter, ln)) -> c20(APP(filter, ln), ENCARG(filter)) ENCARG(cons_app(filter2, ln)) -> c20(APP(filter2, ln), ENCARG(filter2)) ENCARG(cons_app(true, ln)) -> c20(APP(true, ln), ENCARG(true)) ENCARG(cons_app(false, ln)) -> c20(APP(false, ln), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), ln)) -> c20(APP(app(encArg(z0), encArg(z1)), ln), ENCARG(cons_app(z0, z1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(D)) ENCARG(cons_app(t, ln)) -> c20(APP(t, ln), ENCARG(t)) ENCARG(cons_app(1, ln)) -> c20(APP(1, ln), ENCARG(1)) ENCARG(cons_app(constant, ln)) -> c20(APP(constant, ln), ENCARG(constant)) ENCARG(cons_app(0, ln)) -> c20(APP(0, ln), ENCARG(0)) ENCARG(cons_app(+, ln)) -> c20(APP(+, ln), ENCARG(+)) ENCARG(cons_app(*, ln)) -> c20(APP(*, ln), ENCARG(*)) ENCARG(cons_app(-, ln)) -> c20(APP(-, ln), ENCARG(-)) ENCARG(cons_app(minus, ln)) -> c20(APP(minus, ln), ENCARG(minus)) ENCARG(cons_app(div, ln)) -> c20(APP(div, ln), ENCARG(div)) ENCARG(cons_app(pow, ln)) -> c20(APP(pow, ln), ENCARG(pow)) ENCARG(cons_app(2, ln)) -> c20(APP(2, ln), ENCARG(2)) ENCARG(cons_app(ln, ln)) -> c20(APP(ln, ln), ENCARG(ln)) ENCARG(cons_app(map, ln)) -> c20(APP(map, ln), ENCARG(map)) ENCARG(cons_app(nil, ln)) -> c20(APP(nil, ln), ENCARG(nil)) ENCARG(cons_app(cons, ln)) -> c20(APP(cons, ln), ENCARG(cons)) ENCARG(cons_app(filter, ln)) -> c20(APP(filter, ln), ENCARG(filter)) ENCARG(cons_app(filter2, ln)) -> c20(APP(filter2, ln), ENCARG(filter2)) ENCARG(cons_app(true, ln)) -> c20(APP(true, ln), ENCARG(true)) ENCARG(cons_app(false, ln)) -> c20(APP(false, ln), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(D)) ENCARG(cons_app(div, ln)) -> c20(APP(div, ln), ENCARG(div)) ENCARG(cons_app(cons, ln)) -> c20(APP(cons, ln), ENCARG(cons)) ENCARG(cons_app(0, ln)) -> c20(APP(0, ln), ENCARG(0)) ENCARG(cons_app(1, ln)) -> c20(APP(1, ln), ENCARG(1)) ENCARG(cons_app(t, ln)) -> c20(APP(t, ln), ENCARG(t)) ENCARG(cons_app(map, ln)) -> c20(APP(map, ln), ENCARG(map)) ENCARG(cons_app(*, ln)) -> c20(APP(*, ln), ENCARG(*)) ENCARG(cons_app(minus, ln)) -> c20(APP(minus, ln), ENCARG(minus)) ENCARG(cons_app(filter2, ln)) -> c20(APP(filter2, ln), ENCARG(filter2)) ENCARG(cons_app(-, ln)) -> c20(APP(-, ln), ENCARG(-)) ENCARG(cons_app(constant, ln)) -> c20(APP(constant, ln), ENCARG(constant)) ENCARG(cons_app(true, ln)) -> c20(APP(true, ln), ENCARG(true)) ENCARG(cons_app(2, ln)) -> c20(APP(2, ln), ENCARG(2)) ENCARG(cons_app(ln, ln)) -> c20(APP(ln, ln), ENCARG(ln)) ENCARG(cons_app(pow, ln)) -> c20(APP(pow, ln), ENCARG(pow)) ENCARG(cons_app(+, ln)) -> c20(APP(+, ln), ENCARG(+)) ENCARG(cons_app(false, ln)) -> c20(APP(false, ln), ENCARG(false)) ENCARG(cons_app(filter, ln)) -> c20(APP(filter, ln), ENCARG(filter)) ENCARG(cons_app(nil, ln)) -> c20(APP(nil, ln), ENCARG(nil)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, map)) -> c20(APP(encArg(x0), map), ENCARG(x0)) by ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(D)) ENCARG(cons_app(t, map)) -> c20(APP(t, map), ENCARG(t)) ENCARG(cons_app(1, map)) -> c20(APP(1, map), ENCARG(1)) ENCARG(cons_app(constant, map)) -> c20(APP(constant, map), ENCARG(constant)) ENCARG(cons_app(0, map)) -> c20(APP(0, map), ENCARG(0)) ENCARG(cons_app(+, map)) -> c20(APP(+, map), ENCARG(+)) ENCARG(cons_app(*, map)) -> c20(APP(*, map), ENCARG(*)) ENCARG(cons_app(-, map)) -> c20(APP(-, map), ENCARG(-)) ENCARG(cons_app(minus, map)) -> c20(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(div, map)) -> c20(APP(div, map), ENCARG(div)) ENCARG(cons_app(pow, map)) -> c20(APP(pow, map), ENCARG(pow)) ENCARG(cons_app(2, map)) -> c20(APP(2, map), ENCARG(2)) ENCARG(cons_app(ln, map)) -> c20(APP(ln, map), ENCARG(ln)) ENCARG(cons_app(map, map)) -> c20(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c20(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c20(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c20(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c20(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(true, map)) -> c20(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c20(APP(false, map), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), map)) -> c20(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(D)) ENCARG(cons_app(t, map)) -> c20(APP(t, map), ENCARG(t)) ENCARG(cons_app(1, map)) -> c20(APP(1, map), ENCARG(1)) ENCARG(cons_app(constant, map)) -> c20(APP(constant, map), ENCARG(constant)) ENCARG(cons_app(0, map)) -> c20(APP(0, map), ENCARG(0)) ENCARG(cons_app(+, map)) -> c20(APP(+, map), ENCARG(+)) ENCARG(cons_app(*, map)) -> c20(APP(*, map), ENCARG(*)) ENCARG(cons_app(-, map)) -> c20(APP(-, map), ENCARG(-)) ENCARG(cons_app(minus, map)) -> c20(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(div, map)) -> c20(APP(div, map), ENCARG(div)) ENCARG(cons_app(pow, map)) -> c20(APP(pow, map), ENCARG(pow)) ENCARG(cons_app(2, map)) -> c20(APP(2, map), ENCARG(2)) ENCARG(cons_app(ln, map)) -> c20(APP(ln, map), ENCARG(ln)) ENCARG(cons_app(map, map)) -> c20(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c20(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c20(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c20(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c20(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(true, map)) -> c20(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c20(APP(false, map), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(-, map)) -> c20(APP(-, map), ENCARG(-)) ENCARG(cons_app(constant, map)) -> c20(APP(constant, map), ENCARG(constant)) ENCARG(cons_app(pow, map)) -> c20(APP(pow, map), ENCARG(pow)) ENCARG(cons_app(cons, map)) -> c20(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(t, map)) -> c20(APP(t, map), ENCARG(t)) ENCARG(cons_app(filter2, map)) -> c20(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(+, map)) -> c20(APP(+, map), ENCARG(+)) ENCARG(cons_app(filter, map)) -> c20(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(ln, map)) -> c20(APP(ln, map), ENCARG(ln)) ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(D)) ENCARG(cons_app(true, map)) -> c20(APP(true, map), ENCARG(true)) ENCARG(cons_app(minus, map)) -> c20(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(div, map)) -> c20(APP(div, map), ENCARG(div)) ENCARG(cons_app(2, map)) -> c20(APP(2, map), ENCARG(2)) ENCARG(cons_app(*, map)) -> c20(APP(*, map), ENCARG(*)) ENCARG(cons_app(1, map)) -> c20(APP(1, map), ENCARG(1)) ENCARG(cons_app(nil, map)) -> c20(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(0, map)) -> c20(APP(0, map), ENCARG(0)) ENCARG(cons_app(false, map)) -> c20(APP(false, map), ENCARG(false)) ENCARG(cons_app(map, map)) -> c20(APP(map, map), ENCARG(map)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c20(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(D)) ENCARG(cons_app(t, nil)) -> c20(APP(t, nil), ENCARG(t)) ENCARG(cons_app(1, nil)) -> c20(APP(1, nil), ENCARG(1)) ENCARG(cons_app(constant, nil)) -> c20(APP(constant, nil), ENCARG(constant)) ENCARG(cons_app(0, nil)) -> c20(APP(0, nil), ENCARG(0)) ENCARG(cons_app(+, nil)) -> c20(APP(+, nil), ENCARG(+)) ENCARG(cons_app(*, nil)) -> c20(APP(*, nil), ENCARG(*)) ENCARG(cons_app(-, nil)) -> c20(APP(-, nil), ENCARG(-)) ENCARG(cons_app(minus, nil)) -> c20(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(div, nil)) -> c20(APP(div, nil), ENCARG(div)) ENCARG(cons_app(pow, nil)) -> c20(APP(pow, nil), ENCARG(pow)) ENCARG(cons_app(2, nil)) -> c20(APP(2, nil), ENCARG(2)) ENCARG(cons_app(ln, nil)) -> c20(APP(ln, nil), ENCARG(ln)) ENCARG(cons_app(map, nil)) -> c20(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c20(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c20(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c20(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c20(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(true, nil)) -> c20(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c20(APP(false, nil), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c20(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(D)) ENCARG(cons_app(t, nil)) -> c20(APP(t, nil), ENCARG(t)) ENCARG(cons_app(1, nil)) -> c20(APP(1, nil), ENCARG(1)) ENCARG(cons_app(constant, nil)) -> c20(APP(constant, nil), ENCARG(constant)) ENCARG(cons_app(0, nil)) -> c20(APP(0, nil), ENCARG(0)) ENCARG(cons_app(+, nil)) -> c20(APP(+, nil), ENCARG(+)) ENCARG(cons_app(*, nil)) -> c20(APP(*, nil), ENCARG(*)) ENCARG(cons_app(-, nil)) -> c20(APP(-, nil), ENCARG(-)) ENCARG(cons_app(minus, nil)) -> c20(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(div, nil)) -> c20(APP(div, nil), ENCARG(div)) ENCARG(cons_app(pow, nil)) -> c20(APP(pow, nil), ENCARG(pow)) ENCARG(cons_app(2, nil)) -> c20(APP(2, nil), ENCARG(2)) ENCARG(cons_app(ln, nil)) -> c20(APP(ln, nil), ENCARG(ln)) ENCARG(cons_app(map, nil)) -> c20(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c20(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c20(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c20(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c20(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(true, nil)) -> c20(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c20(APP(false, nil), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(minus, nil)) -> c20(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(t, nil)) -> c20(APP(t, nil), ENCARG(t)) ENCARG(cons_app(filter2, nil)) -> c20(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(div, nil)) -> c20(APP(div, nil), ENCARG(div)) ENCARG(cons_app(+, nil)) -> c20(APP(+, nil), ENCARG(+)) ENCARG(cons_app(true, nil)) -> c20(APP(true, nil), ENCARG(true)) ENCARG(cons_app(-, nil)) -> c20(APP(-, nil), ENCARG(-)) ENCARG(cons_app(constant, nil)) -> c20(APP(constant, nil), ENCARG(constant)) ENCARG(cons_app(cons, nil)) -> c20(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(pow, nil)) -> c20(APP(pow, nil), ENCARG(pow)) ENCARG(cons_app(filter, nil)) -> c20(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(map, nil)) -> c20(APP(map, nil), ENCARG(map)) ENCARG(cons_app(ln, nil)) -> c20(APP(ln, nil), ENCARG(ln)) ENCARG(cons_app(1, nil)) -> c20(APP(1, nil), ENCARG(1)) ENCARG(cons_app(*, nil)) -> c20(APP(*, nil), ENCARG(*)) ENCARG(cons_app(2, nil)) -> c20(APP(2, nil), ENCARG(2)) ENCARG(cons_app(0, nil)) -> c20(APP(0, nil), ENCARG(0)) ENCARG(cons_app(nil, nil)) -> c20(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(false, nil)) -> c20(APP(false, nil), ENCARG(false)) ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(D)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c20(APP(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(D)) ENCARG(cons_app(t, cons)) -> c20(APP(t, cons), ENCARG(t)) ENCARG(cons_app(1, cons)) -> c20(APP(1, cons), ENCARG(1)) ENCARG(cons_app(constant, cons)) -> c20(APP(constant, cons), ENCARG(constant)) ENCARG(cons_app(0, cons)) -> c20(APP(0, cons), ENCARG(0)) ENCARG(cons_app(+, cons)) -> c20(APP(+, cons), ENCARG(+)) ENCARG(cons_app(*, cons)) -> c20(APP(*, cons), ENCARG(*)) ENCARG(cons_app(-, cons)) -> c20(APP(-, cons), ENCARG(-)) ENCARG(cons_app(minus, cons)) -> c20(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(div, cons)) -> c20(APP(div, cons), ENCARG(div)) ENCARG(cons_app(pow, cons)) -> c20(APP(pow, cons), ENCARG(pow)) ENCARG(cons_app(2, cons)) -> c20(APP(2, cons), ENCARG(2)) ENCARG(cons_app(ln, cons)) -> c20(APP(ln, cons), ENCARG(ln)) ENCARG(cons_app(map, cons)) -> c20(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c20(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c20(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c20(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c20(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(true, cons)) -> c20(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c20(APP(false, cons), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), cons)) -> c20(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(D)) ENCARG(cons_app(t, cons)) -> c20(APP(t, cons), ENCARG(t)) ENCARG(cons_app(1, cons)) -> c20(APP(1, cons), ENCARG(1)) ENCARG(cons_app(constant, cons)) -> c20(APP(constant, cons), ENCARG(constant)) ENCARG(cons_app(0, cons)) -> c20(APP(0, cons), ENCARG(0)) ENCARG(cons_app(+, cons)) -> c20(APP(+, cons), ENCARG(+)) ENCARG(cons_app(*, cons)) -> c20(APP(*, cons), ENCARG(*)) ENCARG(cons_app(-, cons)) -> c20(APP(-, cons), ENCARG(-)) ENCARG(cons_app(minus, cons)) -> c20(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(div, cons)) -> c20(APP(div, cons), ENCARG(div)) ENCARG(cons_app(pow, cons)) -> c20(APP(pow, cons), ENCARG(pow)) ENCARG(cons_app(2, cons)) -> c20(APP(2, cons), ENCARG(2)) ENCARG(cons_app(ln, cons)) -> c20(APP(ln, cons), ENCARG(ln)) ENCARG(cons_app(map, cons)) -> c20(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c20(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c20(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c20(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c20(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(true, cons)) -> c20(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c20(APP(false, cons), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(t, cons)) -> c20(APP(t, cons), ENCARG(t)) ENCARG(cons_app(0, cons)) -> c20(APP(0, cons), ENCARG(0)) ENCARG(cons_app(2, cons)) -> c20(APP(2, cons), ENCARG(2)) ENCARG(cons_app(pow, cons)) -> c20(APP(pow, cons), ENCARG(pow)) ENCARG(cons_app(*, cons)) -> c20(APP(*, cons), ENCARG(*)) ENCARG(cons_app(-, cons)) -> c20(APP(-, cons), ENCARG(-)) ENCARG(cons_app(constant, cons)) -> c20(APP(constant, cons), ENCARG(constant)) ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(D)) ENCARG(cons_app(div, cons)) -> c20(APP(div, cons), ENCARG(div)) ENCARG(cons_app(nil, cons)) -> c20(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c20(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(minus, cons)) -> c20(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(ln, cons)) -> c20(APP(ln, cons), ENCARG(ln)) ENCARG(cons_app(1, cons)) -> c20(APP(1, cons), ENCARG(1)) ENCARG(cons_app(false, cons)) -> c20(APP(false, cons), ENCARG(false)) ENCARG(cons_app(+, cons)) -> c20(APP(+, cons), ENCARG(+)) ENCARG(cons_app(map, cons)) -> c20(APP(map, cons), ENCARG(map)) ENCARG(cons_app(filter, cons)) -> c20(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(true, cons)) -> c20(APP(true, cons), ENCARG(true)) ENCARG(cons_app(filter2, cons)) -> c20(APP(filter2, cons), ENCARG(filter2)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c20(APP(encArg(x0), filter), ENCARG(x0)) by ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(D)) ENCARG(cons_app(t, filter)) -> c20(APP(t, filter), ENCARG(t)) ENCARG(cons_app(1, filter)) -> c20(APP(1, filter), ENCARG(1)) ENCARG(cons_app(constant, filter)) -> c20(APP(constant, filter), ENCARG(constant)) ENCARG(cons_app(0, filter)) -> c20(APP(0, filter), ENCARG(0)) ENCARG(cons_app(+, filter)) -> c20(APP(+, filter), ENCARG(+)) ENCARG(cons_app(*, filter)) -> c20(APP(*, filter), ENCARG(*)) ENCARG(cons_app(-, filter)) -> c20(APP(-, filter), ENCARG(-)) ENCARG(cons_app(minus, filter)) -> c20(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(div, filter)) -> c20(APP(div, filter), ENCARG(div)) ENCARG(cons_app(pow, filter)) -> c20(APP(pow, filter), ENCARG(pow)) ENCARG(cons_app(2, filter)) -> c20(APP(2, filter), ENCARG(2)) ENCARG(cons_app(ln, filter)) -> c20(APP(ln, filter), ENCARG(ln)) ENCARG(cons_app(map, filter)) -> c20(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c20(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c20(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c20(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c20(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(true, filter)) -> c20(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c20(APP(false, filter), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), filter)) -> c20(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(D)) ENCARG(cons_app(t, filter)) -> c20(APP(t, filter), ENCARG(t)) ENCARG(cons_app(1, filter)) -> c20(APP(1, filter), ENCARG(1)) ENCARG(cons_app(constant, filter)) -> c20(APP(constant, filter), ENCARG(constant)) ENCARG(cons_app(0, filter)) -> c20(APP(0, filter), ENCARG(0)) ENCARG(cons_app(+, filter)) -> c20(APP(+, filter), ENCARG(+)) ENCARG(cons_app(*, filter)) -> c20(APP(*, filter), ENCARG(*)) ENCARG(cons_app(-, filter)) -> c20(APP(-, filter), ENCARG(-)) ENCARG(cons_app(minus, filter)) -> c20(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(div, filter)) -> c20(APP(div, filter), ENCARG(div)) ENCARG(cons_app(pow, filter)) -> c20(APP(pow, filter), ENCARG(pow)) ENCARG(cons_app(2, filter)) -> c20(APP(2, filter), ENCARG(2)) ENCARG(cons_app(ln, filter)) -> c20(APP(ln, filter), ENCARG(ln)) ENCARG(cons_app(map, filter)) -> c20(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c20(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c20(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c20(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c20(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(true, filter)) -> c20(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c20(APP(false, filter), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(*, filter)) -> c20(APP(*, filter), ENCARG(*)) ENCARG(cons_app(0, filter)) -> c20(APP(0, filter), ENCARG(0)) ENCARG(cons_app(true, filter)) -> c20(APP(true, filter), ENCARG(true)) ENCARG(cons_app(cons, filter)) -> c20(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(2, filter)) -> c20(APP(2, filter), ENCARG(2)) ENCARG(cons_app(ln, filter)) -> c20(APP(ln, filter), ENCARG(ln)) ENCARG(cons_app(div, filter)) -> c20(APP(div, filter), ENCARG(div)) ENCARG(cons_app(+, filter)) -> c20(APP(+, filter), ENCARG(+)) ENCARG(cons_app(nil, filter)) -> c20(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(false, filter)) -> c20(APP(false, filter), ENCARG(false)) ENCARG(cons_app(filter, filter)) -> c20(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(D)) ENCARG(cons_app(map, filter)) -> c20(APP(map, filter), ENCARG(map)) ENCARG(cons_app(minus, filter)) -> c20(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(pow, filter)) -> c20(APP(pow, filter), ENCARG(pow)) ENCARG(cons_app(1, filter)) -> c20(APP(1, filter), ENCARG(1)) ENCARG(cons_app(t, filter)) -> c20(APP(t, filter), ENCARG(t)) ENCARG(cons_app(-, filter)) -> c20(APP(-, filter), ENCARG(-)) ENCARG(cons_app(constant, filter)) -> c20(APP(constant, filter), ENCARG(constant)) ENCARG(cons_app(filter2, filter)) -> c20(APP(filter2, filter), ENCARG(filter2)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c20(APP(encArg(x0), filter2), ENCARG(x0)) by ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(D)) ENCARG(cons_app(t, filter2)) -> c20(APP(t, filter2), ENCARG(t)) ENCARG(cons_app(1, filter2)) -> c20(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(constant, filter2)) -> c20(APP(constant, filter2), ENCARG(constant)) ENCARG(cons_app(0, filter2)) -> c20(APP(0, filter2), ENCARG(0)) ENCARG(cons_app(+, filter2)) -> c20(APP(+, filter2), ENCARG(+)) ENCARG(cons_app(*, filter2)) -> c20(APP(*, filter2), ENCARG(*)) ENCARG(cons_app(-, filter2)) -> c20(APP(-, filter2), ENCARG(-)) ENCARG(cons_app(minus, filter2)) -> c20(APP(minus, filter2), ENCARG(minus)) ENCARG(cons_app(div, filter2)) -> c20(APP(div, filter2), ENCARG(div)) ENCARG(cons_app(pow, filter2)) -> c20(APP(pow, filter2), ENCARG(pow)) ENCARG(cons_app(2, filter2)) -> c20(APP(2, filter2), ENCARG(2)) ENCARG(cons_app(ln, filter2)) -> c20(APP(ln, filter2), ENCARG(ln)) ENCARG(cons_app(map, filter2)) -> c20(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(nil, filter2)) -> c20(APP(nil, filter2), ENCARG(nil)) ENCARG(cons_app(cons, filter2)) -> c20(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(filter, filter2)) -> c20(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(filter2, filter2)) -> c20(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(true, filter2)) -> c20(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(false, filter2)) -> c20(APP(false, filter2), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c20(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(D)) ENCARG(cons_app(t, filter2)) -> c20(APP(t, filter2), ENCARG(t)) ENCARG(cons_app(1, filter2)) -> c20(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(constant, filter2)) -> c20(APP(constant, filter2), ENCARG(constant)) ENCARG(cons_app(0, filter2)) -> c20(APP(0, filter2), ENCARG(0)) ENCARG(cons_app(+, filter2)) -> c20(APP(+, filter2), ENCARG(+)) ENCARG(cons_app(*, filter2)) -> c20(APP(*, filter2), ENCARG(*)) ENCARG(cons_app(-, filter2)) -> c20(APP(-, filter2), ENCARG(-)) ENCARG(cons_app(minus, filter2)) -> c20(APP(minus, filter2), ENCARG(minus)) ENCARG(cons_app(div, filter2)) -> c20(APP(div, filter2), ENCARG(div)) ENCARG(cons_app(pow, filter2)) -> c20(APP(pow, filter2), ENCARG(pow)) ENCARG(cons_app(2, filter2)) -> c20(APP(2, filter2), ENCARG(2)) ENCARG(cons_app(ln, filter2)) -> c20(APP(ln, filter2), ENCARG(ln)) ENCARG(cons_app(map, filter2)) -> c20(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(nil, filter2)) -> c20(APP(nil, filter2), ENCARG(nil)) ENCARG(cons_app(cons, filter2)) -> c20(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(filter, filter2)) -> c20(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(filter2, filter2)) -> c20(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(true, filter2)) -> c20(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(false, filter2)) -> c20(APP(false, filter2), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(map, filter2)) -> c20(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(nil, filter2)) -> c20(APP(nil, filter2), ENCARG(nil)) ENCARG(cons_app(cons, filter2)) -> c20(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(ln, filter2)) -> c20(APP(ln, filter2), ENCARG(ln)) ENCARG(cons_app(t, filter2)) -> c20(APP(t, filter2), ENCARG(t)) ENCARG(cons_app(minus, filter2)) -> c20(APP(minus, filter2), ENCARG(minus)) ENCARG(cons_app(-, filter2)) -> c20(APP(-, filter2), ENCARG(-)) ENCARG(cons_app(constant, filter2)) -> c20(APP(constant, filter2), ENCARG(constant)) ENCARG(cons_app(2, filter2)) -> c20(APP(2, filter2), ENCARG(2)) ENCARG(cons_app(pow, filter2)) -> c20(APP(pow, filter2), ENCARG(pow)) ENCARG(cons_app(+, filter2)) -> c20(APP(+, filter2), ENCARG(+)) ENCARG(cons_app(*, filter2)) -> c20(APP(*, filter2), ENCARG(*)) ENCARG(cons_app(0, filter2)) -> c20(APP(0, filter2), ENCARG(0)) ENCARG(cons_app(filter, filter2)) -> c20(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(div, filter2)) -> c20(APP(div, filter2), ENCARG(div)) ENCARG(cons_app(1, filter2)) -> c20(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(true, filter2)) -> c20(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(filter2, filter2)) -> c20(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(false, filter2)) -> c20(APP(false, filter2), ENCARG(false)) ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(D)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c20(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(D)) ENCARG(cons_app(t, true)) -> c20(APP(t, true), ENCARG(t)) ENCARG(cons_app(1, true)) -> c20(APP(1, true), ENCARG(1)) ENCARG(cons_app(constant, true)) -> c20(APP(constant, true), ENCARG(constant)) ENCARG(cons_app(0, true)) -> c20(APP(0, true), ENCARG(0)) ENCARG(cons_app(+, true)) -> c20(APP(+, true), ENCARG(+)) ENCARG(cons_app(*, true)) -> c20(APP(*, true), ENCARG(*)) ENCARG(cons_app(-, true)) -> c20(APP(-, true), ENCARG(-)) ENCARG(cons_app(minus, true)) -> c20(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(div, true)) -> c20(APP(div, true), ENCARG(div)) ENCARG(cons_app(pow, true)) -> c20(APP(pow, true), ENCARG(pow)) ENCARG(cons_app(2, true)) -> c20(APP(2, true), ENCARG(2)) ENCARG(cons_app(ln, true)) -> c20(APP(ln, true), ENCARG(ln)) ENCARG(cons_app(map, true)) -> c20(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c20(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c20(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c20(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c20(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(true, true)) -> c20(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c20(APP(false, true), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c20(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(D)) ENCARG(cons_app(t, true)) -> c20(APP(t, true), ENCARG(t)) ENCARG(cons_app(1, true)) -> c20(APP(1, true), ENCARG(1)) ENCARG(cons_app(constant, true)) -> c20(APP(constant, true), ENCARG(constant)) ENCARG(cons_app(0, true)) -> c20(APP(0, true), ENCARG(0)) ENCARG(cons_app(+, true)) -> c20(APP(+, true), ENCARG(+)) ENCARG(cons_app(*, true)) -> c20(APP(*, true), ENCARG(*)) ENCARG(cons_app(-, true)) -> c20(APP(-, true), ENCARG(-)) ENCARG(cons_app(minus, true)) -> c20(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(div, true)) -> c20(APP(div, true), ENCARG(div)) ENCARG(cons_app(pow, true)) -> c20(APP(pow, true), ENCARG(pow)) ENCARG(cons_app(2, true)) -> c20(APP(2, true), ENCARG(2)) ENCARG(cons_app(ln, true)) -> c20(APP(ln, true), ENCARG(ln)) ENCARG(cons_app(map, true)) -> c20(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c20(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c20(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c20(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c20(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(true, true)) -> c20(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c20(APP(false, true), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(ln, true)) -> c20(APP(ln, true), ENCARG(ln)) ENCARG(cons_app(*, true)) -> c20(APP(*, true), ENCARG(*)) ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(D)) ENCARG(cons_app(cons, true)) -> c20(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(map, true)) -> c20(APP(map, true), ENCARG(map)) ENCARG(cons_app(1, true)) -> c20(APP(1, true), ENCARG(1)) ENCARG(cons_app(+, true)) -> c20(APP(+, true), ENCARG(+)) ENCARG(cons_app(2, true)) -> c20(APP(2, true), ENCARG(2)) ENCARG(cons_app(false, true)) -> c20(APP(false, true), ENCARG(false)) ENCARG(cons_app(pow, true)) -> c20(APP(pow, true), ENCARG(pow)) ENCARG(cons_app(0, true)) -> c20(APP(0, true), ENCARG(0)) ENCARG(cons_app(nil, true)) -> c20(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(minus, true)) -> c20(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(-, true)) -> c20(APP(-, true), ENCARG(-)) ENCARG(cons_app(constant, true)) -> c20(APP(constant, true), ENCARG(constant)) ENCARG(cons_app(true, true)) -> c20(APP(true, true), ENCARG(true)) ENCARG(cons_app(div, true)) -> c20(APP(div, true), ENCARG(div)) ENCARG(cons_app(filter2, true)) -> c20(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(filter, true)) -> c20(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(t, true)) -> c20(APP(t, true), ENCARG(t)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c20(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(D)) ENCARG(cons_app(t, false)) -> c20(APP(t, false), ENCARG(t)) ENCARG(cons_app(1, false)) -> c20(APP(1, false), ENCARG(1)) ENCARG(cons_app(constant, false)) -> c20(APP(constant, false), ENCARG(constant)) ENCARG(cons_app(0, false)) -> c20(APP(0, false), ENCARG(0)) ENCARG(cons_app(+, false)) -> c20(APP(+, false), ENCARG(+)) ENCARG(cons_app(*, false)) -> c20(APP(*, false), ENCARG(*)) ENCARG(cons_app(-, false)) -> c20(APP(-, false), ENCARG(-)) ENCARG(cons_app(minus, false)) -> c20(APP(minus, false), ENCARG(minus)) ENCARG(cons_app(div, false)) -> c20(APP(div, false), ENCARG(div)) ENCARG(cons_app(pow, false)) -> c20(APP(pow, false), ENCARG(pow)) ENCARG(cons_app(2, false)) -> c20(APP(2, false), ENCARG(2)) ENCARG(cons_app(ln, false)) -> c20(APP(ln, false), ENCARG(ln)) ENCARG(cons_app(map, false)) -> c20(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c20(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c20(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c20(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c20(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(true, false)) -> c20(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c20(APP(false, false), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c20(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(D)) ENCARG(cons_app(t, false)) -> c20(APP(t, false), ENCARG(t)) ENCARG(cons_app(1, false)) -> c20(APP(1, false), ENCARG(1)) ENCARG(cons_app(constant, false)) -> c20(APP(constant, false), ENCARG(constant)) ENCARG(cons_app(0, false)) -> c20(APP(0, false), ENCARG(0)) ENCARG(cons_app(+, false)) -> c20(APP(+, false), ENCARG(+)) ENCARG(cons_app(*, false)) -> c20(APP(*, false), ENCARG(*)) ENCARG(cons_app(-, false)) -> c20(APP(-, false), ENCARG(-)) ENCARG(cons_app(minus, false)) -> c20(APP(minus, false), ENCARG(minus)) ENCARG(cons_app(div, false)) -> c20(APP(div, false), ENCARG(div)) ENCARG(cons_app(pow, false)) -> c20(APP(pow, false), ENCARG(pow)) ENCARG(cons_app(2, false)) -> c20(APP(2, false), ENCARG(2)) ENCARG(cons_app(ln, false)) -> c20(APP(ln, false), ENCARG(ln)) ENCARG(cons_app(map, false)) -> c20(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c20(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c20(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c20(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c20(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(true, false)) -> c20(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c20(APP(false, false), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCARG(cons_app(filter, false)) -> c20(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(+, false)) -> c20(APP(+, false), ENCARG(+)) ENCARG(cons_app(-, false)) -> c20(APP(-, false), ENCARG(-)) ENCARG(cons_app(*, false)) -> c20(APP(*, false), ENCARG(*)) ENCARG(cons_app(constant, false)) -> c20(APP(constant, false), ENCARG(constant)) ENCARG(cons_app(t, false)) -> c20(APP(t, false), ENCARG(t)) ENCARG(cons_app(nil, false)) -> c20(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(filter2, false)) -> c20(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(minus, false)) -> c20(APP(minus, false), ENCARG(minus)) ENCARG(cons_app(div, false)) -> c20(APP(div, false), ENCARG(div)) ENCARG(cons_app(1, false)) -> c20(APP(1, false), ENCARG(1)) ENCARG(cons_app(false, false)) -> c20(APP(false, false), ENCARG(false)) ENCARG(cons_app(map, false)) -> c20(APP(map, false), ENCARG(map)) ENCARG(cons_app(0, false)) -> c20(APP(0, false), ENCARG(0)) ENCARG(cons_app(pow, false)) -> c20(APP(pow, false), ENCARG(pow)) ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(D)) ENCARG(cons_app(cons, false)) -> c20(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(2, false)) -> c20(APP(2, false), ENCARG(2)) ENCARG(cons_app(true, false)) -> c20(APP(true, false), ENCARG(true)) ENCARG(cons_app(ln, false)) -> c20(APP(ln, false), ENCARG(ln)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_2, c20_1, c54_2, c54_1, c_1, c20_3 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(D, x1)) -> c20(APP(D, encArg(x1)), ENCARG(x1)) by ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(t)) ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(1)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(constant)) ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(0)) ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(+)) ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(*)) ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(-)) ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(minus)) ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(div)) ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(pow)) ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(2)) ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(ln)) ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(map)) ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(nil)) ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(cons)) ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(filter)) ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(filter2)) ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(true)) ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(false)) ENCARG(cons_app(D, cons_app(z0, z1))) -> c20(APP(D, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(t)) ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(1)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(constant)) ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(0)) ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(+)) ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(*)) ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(-)) ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(minus)) ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(div)) ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(pow)) ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(2)) ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(ln)) ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(map)) ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(nil)) ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(cons)) ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(filter)) ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(filter2)) ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(true)) ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(false)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_1, c54_2, c54_1, c_1, c20_3, c20_2 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 18 trailing nodes: ENCARG(cons_app(D, nil)) -> c20(APP(D, nil), ENCARG(nil)) ENCARG(cons_app(D, cons)) -> c20(APP(D, cons), ENCARG(cons)) ENCARG(cons_app(D, 2)) -> c20(APP(D, 2), ENCARG(2)) ENCARG(cons_app(D, +)) -> c20(APP(D, +), ENCARG(+)) ENCARG(cons_app(D, 0)) -> c20(APP(D, 0), ENCARG(0)) ENCARG(cons_app(D, 1)) -> c20(APP(D, 1), ENCARG(1)) ENCARG(cons_app(D, true)) -> c20(APP(D, true), ENCARG(true)) ENCARG(cons_app(D, div)) -> c20(APP(D, div), ENCARG(div)) ENCARG(cons_app(D, minus)) -> c20(APP(D, minus), ENCARG(minus)) ENCARG(cons_app(D, D)) -> c20(APP(D, D), ENCARG(D)) ENCARG(cons_app(D, pow)) -> c20(APP(D, pow), ENCARG(pow)) ENCARG(cons_app(D, filter)) -> c20(APP(D, filter), ENCARG(filter)) ENCARG(cons_app(D, map)) -> c20(APP(D, map), ENCARG(map)) ENCARG(cons_app(D, -)) -> c20(APP(D, -), ENCARG(-)) ENCARG(cons_app(D, filter2)) -> c20(APP(D, filter2), ENCARG(filter2)) ENCARG(cons_app(D, ln)) -> c20(APP(D, ln), ENCARG(ln)) ENCARG(cons_app(D, false)) -> c20(APP(D, false), ENCARG(false)) ENCARG(cons_app(D, *)) -> c20(APP(D, *), ENCARG(*)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) ENCARG(cons_app(D, t)) -> c20(APP(D, t), ENCARG(t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant), ENCARG(constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_1, c54_2, c54_1, c_1, c20_3, c20_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(D) -> D encArg(t) -> t encArg(1) -> 1 encArg(constant) -> constant encArg(0) -> 0 encArg(+) -> + encArg(*) -> * encArg(-) -> - encArg(minus) -> minus encArg(div) -> div encArg(pow) -> pow encArg(2) -> 2 encArg(ln) -> ln encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(D, t) -> 1 app(D, constant) -> 0 app(D, app(app(+, z0), z1)) -> app(app(+, app(D, z0)), app(D, z1)) app(D, app(app(*, z0), z1)) -> app(app(+, app(app(*, z1), app(D, z0))), app(app(*, z0), app(D, z1))) app(D, app(app(-, z0), z1)) -> app(app(-, app(D, z0)), app(D, z1)) app(D, app(minus, z0)) -> app(minus, app(D, z0)) app(D, app(app(div, z0), z1)) -> app(app(-, app(app(div, app(D, z0)), z1)), app(app(div, app(app(*, z0), app(D, z1))), app(app(pow, z1), 2))) app(D, app(ln, z0)) -> app(app(div, app(D, z0)), z0) app(D, app(app(pow, z0), z1)) -> app(app(+, app(app(*, app(app(*, z1), app(app(pow, z0), app(app(-, z1), 1)))), app(D, z0))), app(app(*, app(app(*, app(app(pow, z0), z1)), app(ln, z0))), app(D, z1))) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) ENCARG(cons_app(t, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(constant, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(+, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(*, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(-, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(minus, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(div, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(pow, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(ln, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c20(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c20(ENCARG(x1)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, D) -> c(APP(encArg(x0), D)) ENCODE_APP(x0, t) -> c(APP(encArg(x0), t)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, constant) -> c(APP(encArg(x0), constant)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, +) -> c(APP(encArg(x0), +)) ENCODE_APP(x0, *) -> c(APP(encArg(x0), *)) ENCODE_APP(x0, -) -> c(APP(encArg(x0), -)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, div) -> c(APP(encArg(x0), div)) ENCODE_APP(x0, pow) -> c(APP(encArg(x0), pow)) ENCODE_APP(x0, 2) -> c(APP(encArg(x0), 2)) ENCODE_APP(x0, ln) -> c(APP(encArg(x0), ln)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(D, x1) -> c(APP(D, 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, D))) -> c20(APP(encArg(x0), app(encArg(x1), D)), ENCARG(x0), ENCARG(cons_app(x1, D))) ENCARG(cons_app(x0, cons_app(x1, t))) -> c20(APP(encArg(x0), app(encArg(x1), t)), ENCARG(x0), ENCARG(cons_app(x1, t))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c20(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, constant))) -> c20(APP(encArg(x0), app(encArg(x1), constant)), ENCARG(x0), ENCARG(cons_app(x1, constant))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c20(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, +))) -> c20(APP(encArg(x0), app(encArg(x1), +)), ENCARG(x0), ENCARG(cons_app(x1, +))) ENCARG(cons_app(x0, cons_app(x1, *))) -> c20(APP(encArg(x0), app(encArg(x1), *)), ENCARG(x0), ENCARG(cons_app(x1, *))) ENCARG(cons_app(x0, cons_app(x1, -))) -> c20(APP(encArg(x0), app(encArg(x1), -)), ENCARG(x0), ENCARG(cons_app(x1, -))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c20(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, div))) -> c20(APP(encArg(x0), app(encArg(x1), div)), ENCARG(x0), ENCARG(cons_app(x1, div))) ENCARG(cons_app(x0, cons_app(x1, pow))) -> c20(APP(encArg(x0), app(encArg(x1), pow)), ENCARG(x0), ENCARG(cons_app(x1, pow))) ENCARG(cons_app(x0, cons_app(x1, 2))) -> c20(APP(encArg(x0), app(encArg(x1), 2)), ENCARG(x0), ENCARG(cons_app(x1, 2))) ENCARG(cons_app(x0, cons_app(x1, ln))) -> c20(APP(encArg(x0), app(encArg(x1), ln)), ENCARG(x0), ENCARG(cons_app(x1, ln))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c20(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c20(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c20(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c20(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c20(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c20(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c20(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c20(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(D, x2))) -> c20(APP(encArg(x0), app(D, encArg(x2))), ENCARG(x0), ENCARG(cons_app(D, x2))) ENCARG(cons_app(x0, cons_app(t, x2))) -> c20(APP(encArg(x0), app(t, encArg(x2))), ENCARG(x0), ENCARG(cons_app(t, x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c20(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(constant, x2))) -> c20(APP(encArg(x0), app(constant, encArg(x2))), ENCARG(x0), ENCARG(cons_app(constant, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c20(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(+, x2))) -> c20(APP(encArg(x0), app(+, encArg(x2))), ENCARG(x0), ENCARG(cons_app(+, x2))) ENCARG(cons_app(x0, cons_app(*, x2))) -> c20(APP(encArg(x0), app(*, encArg(x2))), ENCARG(x0), ENCARG(cons_app(*, x2))) ENCARG(cons_app(x0, cons_app(-, x2))) -> c20(APP(encArg(x0), app(-, encArg(x2))), ENCARG(x0), ENCARG(cons_app(-, x2))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c20(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(div, x2))) -> c20(APP(encArg(x0), app(div, encArg(x2))), ENCARG(x0), ENCARG(cons_app(div, x2))) ENCARG(cons_app(x0, cons_app(pow, x2))) -> c20(APP(encArg(x0), app(pow, encArg(x2))), ENCARG(x0), ENCARG(cons_app(pow, x2))) ENCARG(cons_app(x0, cons_app(2, x2))) -> c20(APP(encArg(x0), app(2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(2, x2))) ENCARG(cons_app(x0, cons_app(ln, x2))) -> c20(APP(encArg(x0), app(ln, encArg(x2))), ENCARG(x0), ENCARG(cons_app(ln, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c20(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c20(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c20(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c20(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c20(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c20(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c20(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c20(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))) -> c20(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(D, cons_app(x1, x2))) -> c20(APP(D, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(t, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(constant, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(+, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(*, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(-, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(div, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(pow, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(ln, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c20(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, D), x2)) -> c20(APP(app(encArg(x0), D), encArg(x2)), ENCARG(cons_app(x0, D)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, t), x2)) -> c20(APP(app(encArg(x0), t), encArg(x2)), ENCARG(cons_app(x0, t)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c20(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, constant), x2)) -> c20(APP(app(encArg(x0), constant), encArg(x2)), ENCARG(cons_app(x0, constant)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c20(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, +), x2)) -> c20(APP(app(encArg(x0), +), encArg(x2)), ENCARG(cons_app(x0, +)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, *), x2)) -> c20(APP(app(encArg(x0), *), encArg(x2)), ENCARG(cons_app(x0, *)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, -), x2)) -> c20(APP(app(encArg(x0), -), encArg(x2)), ENCARG(cons_app(x0, -)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c20(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, div), x2)) -> c20(APP(app(encArg(x0), div), encArg(x2)), ENCARG(cons_app(x0, div)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, pow), x2)) -> c20(APP(app(encArg(x0), pow), encArg(x2)), ENCARG(cons_app(x0, pow)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 2), x2)) -> c20(APP(app(encArg(x0), 2), encArg(x2)), ENCARG(cons_app(x0, 2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, ln), x2)) -> c20(APP(app(encArg(x0), ln), encArg(x2)), ENCARG(cons_app(x0, ln)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c20(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c20(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c20(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c20(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c20(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c20(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c20(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c20(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(D, x1), x2)) -> c20(APP(app(D, encArg(x1)), encArg(x2)), ENCARG(cons_app(D, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c20(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c20(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)) -> c20(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), D)) -> c20(APP(app(encArg(x0), encArg(x1)), D), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), t)) -> c20(APP(app(encArg(x0), encArg(x1)), t), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c20(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), constant)) -> c20(APP(app(encArg(x0), encArg(x1)), constant), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c20(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), +)) -> c20(APP(app(encArg(x0), encArg(x1)), +), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), *)) -> c20(APP(app(encArg(x0), encArg(x1)), *), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), -)) -> c20(APP(app(encArg(x0), encArg(x1)), -), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c20(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), div)) -> c20(APP(app(encArg(x0), encArg(x1)), div), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), pow)) -> c20(APP(app(encArg(x0), encArg(x1)), pow), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 2)) -> c20(APP(app(encArg(x0), encArg(x1)), 2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), ln)) -> c20(APP(app(encArg(x0), encArg(x1)), ln), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c20(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c20(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c20(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c20(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c20(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c20(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c20(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(t, x1), x2)) -> c20(ENCARG(cons_app(t, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c20(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(constant, x1), x2)) -> c20(ENCARG(cons_app(constant, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c20(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(+, x1), x2)) -> c20(ENCARG(cons_app(+, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(*, x1), x2)) -> c20(ENCARG(cons_app(*, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(-, x1), x2)) -> c20(ENCARG(cons_app(-, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c20(ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(div, x1), x2)) -> c20(ENCARG(cons_app(div, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(pow, x1), x2)) -> c20(ENCARG(cons_app(pow, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(2, x1), x2)) -> c20(ENCARG(cons_app(2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(ln, x1), x2)) -> c20(ENCARG(cons_app(ln, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c20(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c20(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c20(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c20(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c20(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(D, t)) -> c20(APP(D, t)) ENCARG(cons_app(D, constant)) -> c20(APP(D, constant)) S tuples: APP(D, t) -> c42 APP(D, constant) -> c43 APP(app(map, z0), nil) -> c51 APP(app(filter, z0), nil) -> c53 APP(D, app(app(+, z0), z1)) -> c44(APP(D, z0), APP(D, z1)) APP(D, app(app(*, z0), z1)) -> c45(APP(D, z0), APP(D, z1)) APP(D, app(app(-, z0), z1)) -> c46(APP(D, z0), APP(D, z1)) APP(D, app(minus, z0)) -> c47(APP(D, z0)) APP(D, app(app(div, z0), z1)) -> c48(APP(D, z0), APP(D, z1)) APP(D, app(ln, z0)) -> c49(APP(D, z0)) APP(D, app(app(pow, z0), z1)) -> c50(APP(D, z0), APP(D, z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c52(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c55(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c56(APP(app(filter, z0), z2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c54(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, D), app(app(cons, t), x2)) -> c54(APP(D, t)) APP(app(filter, D), app(app(cons, constant), x2)) -> c54(APP(D, constant)) APP(app(filter, D), app(app(cons, app(app(+, z0), z1)), x2)) -> c54(APP(D, app(app(+, z0), z1))) APP(app(filter, D), app(app(cons, app(app(*, z0), z1)), x2)) -> c54(APP(D, app(app(*, z0), z1))) APP(app(filter, D), app(app(cons, app(app(-, z0), z1)), x2)) -> c54(APP(D, app(app(-, z0), z1))) APP(app(filter, D), app(app(cons, app(minus, z0)), x2)) -> c54(APP(D, app(minus, z0))) APP(app(filter, D), app(app(cons, app(app(div, z0), z1)), x2)) -> c54(APP(D, app(app(div, z0), z1))) APP(app(filter, D), app(app(cons, app(ln, z0)), x2)) -> c54(APP(D, app(ln, z0))) APP(app(filter, D), app(app(cons, app(app(pow, z0), z1)), x2)) -> c54(APP(D, app(app(pow, z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c54(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c54(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c54(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c54(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: c42, c43, c51, c53, c44_2, c45_2, c46_2, c47_1, c48_2, c49_1, c50_2, c52_2, c55_1, c56_1, c20_1, c54_2, c54_1, c_1, c20_3, c20_2