KILLED proof of input_0NTiGzurUq.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (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), 6 ms] (12) typed CpxTrs (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) RelTrsToWeightedTrsProof [UPPER BOUND(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), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) InliningProof [UPPER BOUND(ID), 128 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxRelTRS (47) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (48) CpxTRS (49) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxWeightedTrs (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxTypedWeightedTrs (53) CompletionProof [UPPER BOUND(ID), 0 ms] (54) CpxTypedWeightedCompleteTrs (55) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxTypedWeightedCompleteTrs (57) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) InliningProof [UPPER BOUND(ID), 215 ms] (60) CpxRNTS (61) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CpxRNTS (63) CompletionProof [UPPER BOUND(ID), 0 ms] (64) CpxTypedWeightedCompleteTrs (65) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (66) CpxRNTS (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 6 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 7 ms] (138) CdtProblem (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 6 ms] (140) CdtProblem (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 11 ms] (156) CdtProblem (157) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 10 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 5 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) nats(N) -> cons(N, n__nats(s(N))) zprimes -> sieve(nats(s(s(0)))) filter(X1, X2, X3) -> n__filter(X1, X2, X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: filter(cons(X, Y), 0', M) -> cons(0', n__filter(activate(Y), M, M)) filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) sieve(cons(0', Y)) -> cons(0', n__sieve(activate(Y))) sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) nats(N) -> cons(N, n__nats(s(N))) zprimes -> sieve(nats(s(s(0')))) filter(X1, X2, X3) -> n__filter(X1, X2, X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 K tuples:none Defined Rule Symbols: filter_3, sieve_1, nats_1, zprimes, activate_1 Defined Pair Symbols: FILTER_3, SIEVE_1, NATS_1, ZPRIMES, ACTIVATE_1 Compound Symbols: c_1, c1_1, c2, c3_1, c4_2, c5, c6, c7, c8_2, c9_1, c10_1, c11_1, c12 ---------------------------------------- (5) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (6) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 The (relative) TRS S consists of the following rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 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: FILTER(cons(z0, z1), 0', z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0', z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0')))), NATS(s(s(0')))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 The (relative) TRS S consists of the following rules: filter(cons(z0, z1), 0', z2) -> cons(0', n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0', z0)) -> cons(0', n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0')))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: FILTER(cons(z0, z1), 0', z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0', z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0')))), NATS(s(s(0')))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 filter(cons(z0, z1), 0', z2) -> cons(0', n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0', z0)) -> cons(0', n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0')))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Types: FILTER :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> c:c1:c2 cons :: 0':s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0' :: 0':s c :: c9:c10:c11:c12 -> c:c1:c2 ACTIVATE :: cons:n__filter:n__sieve:n__nats -> c9:c10:c11:c12 s :: 0':s -> 0':s c1 :: c9:c10:c11:c12 -> c:c1:c2 c2 :: c:c1:c2 SIEVE :: cons:n__filter:n__sieve:n__nats -> c3:c4:c5 c3 :: c9:c10:c11:c12 -> c3:c4:c5 c4 :: c:c1:c2 -> c9:c10:c11:c12 -> c3:c4:c5 activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats c5 :: c3:c4:c5 NATS :: 0':s -> c6:c7 c6 :: c6:c7 c7 :: c6:c7 ZPRIMES :: c8 c8 :: c3:c4:c5 -> c6:c7 -> c8 nats :: 0':s -> cons:n__filter:n__sieve:n__nats n__filter :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> cons:n__filter:n__sieve:n__nats c9 :: c:c1:c2 -> c9:c10:c11:c12 n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats c10 :: c3:c4:c5 -> c9:c10:c11:c12 n__nats :: 0':s -> cons:n__filter:n__sieve:n__nats c11 :: c6:c7 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 filter :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> cons:n__filter:n__sieve:n__nats sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats hole_c:c1:c21_13 :: c:c1:c2 hole_cons:n__filter:n__sieve:n__nats2_13 :: cons:n__filter:n__sieve:n__nats hole_0':s3_13 :: 0':s hole_c9:c10:c11:c124_13 :: c9:c10:c11:c12 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c6:c76_13 :: c6:c7 hole_c87_13 :: c8 gen_cons:n__filter:n__sieve:n__nats8_13 :: Nat -> cons:n__filter:n__sieve:n__nats gen_0':s9_13 :: Nat -> 0':s ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: FILTER, ACTIVATE, SIEVE, activate, filter, sieve They will be analysed ascendingly in the following order: FILTER = ACTIVATE FILTER = SIEVE ACTIVATE = SIEVE activate < SIEVE activate = filter activate = sieve filter = sieve ---------------------------------------- (12) Obligation: Innermost TRS: Rules: FILTER(cons(z0, z1), 0', z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0', z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0')))), NATS(s(s(0')))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 filter(cons(z0, z1), 0', z2) -> cons(0', n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0', z0)) -> cons(0', n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0')))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Types: FILTER :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> c:c1:c2 cons :: 0':s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0' :: 0':s c :: c9:c10:c11:c12 -> c:c1:c2 ACTIVATE :: cons:n__filter:n__sieve:n__nats -> c9:c10:c11:c12 s :: 0':s -> 0':s c1 :: c9:c10:c11:c12 -> c:c1:c2 c2 :: c:c1:c2 SIEVE :: cons:n__filter:n__sieve:n__nats -> c3:c4:c5 c3 :: c9:c10:c11:c12 -> c3:c4:c5 c4 :: c:c1:c2 -> c9:c10:c11:c12 -> c3:c4:c5 activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats c5 :: c3:c4:c5 NATS :: 0':s -> c6:c7 c6 :: c6:c7 c7 :: c6:c7 ZPRIMES :: c8 c8 :: c3:c4:c5 -> c6:c7 -> c8 nats :: 0':s -> cons:n__filter:n__sieve:n__nats n__filter :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> cons:n__filter:n__sieve:n__nats c9 :: c:c1:c2 -> c9:c10:c11:c12 n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats c10 :: c3:c4:c5 -> c9:c10:c11:c12 n__nats :: 0':s -> cons:n__filter:n__sieve:n__nats c11 :: c6:c7 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 filter :: cons:n__filter:n__sieve:n__nats -> 0':s -> 0':s -> cons:n__filter:n__sieve:n__nats sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats hole_c:c1:c21_13 :: c:c1:c2 hole_cons:n__filter:n__sieve:n__nats2_13 :: cons:n__filter:n__sieve:n__nats hole_0':s3_13 :: 0':s hole_c9:c10:c11:c124_13 :: c9:c10:c11:c12 hole_c3:c4:c55_13 :: c3:c4:c5 hole_c6:c76_13 :: c6:c7 hole_c87_13 :: c8 gen_cons:n__filter:n__sieve:n__nats8_13 :: Nat -> cons:n__filter:n__sieve:n__nats gen_0':s9_13 :: Nat -> 0':s Generator Equations: gen_cons:n__filter:n__sieve:n__nats8_13(0) <=> n__nats(0') gen_cons:n__filter:n__sieve:n__nats8_13(+(x, 1)) <=> cons(0', gen_cons:n__filter:n__sieve:n__nats8_13(x)) gen_0':s9_13(0) <=> 0' gen_0':s9_13(+(x, 1)) <=> s(gen_0':s9_13(x)) The following defined symbols remain to be analysed: filter, FILTER, ACTIVATE, SIEVE, activate, sieve They will be analysed ascendingly in the following order: FILTER = ACTIVATE FILTER = SIEVE ACTIVATE = SIEVE activate < SIEVE activate = filter activate = sieve filter = sieve ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 The (relative) TRS S consists of the following rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) nats(N) -> cons(N, n__nats(s(N))) zprimes -> sieve(nats(s(s(0)))) filter(X1, X2, X3) -> n__filter(X1, X2, X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (UPPER BOUND(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: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) [1] filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) [1] sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) [1] sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) [1] nats(N) -> cons(N, n__nats(s(N))) [1] zprimes -> sieve(nats(s(s(0)))) [1] filter(X1, X2, X3) -> n__filter(X1, X2, X3) [1] sieve(X) -> n__sieve(X) [1] nats(X) -> n__nats(X) [1] activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) [1] activate(n__sieve(X)) -> sieve(X) [1] activate(n__nats(X)) -> nats(X) [1] activate(X) -> X [1] 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: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) [1] filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) [1] sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) [1] sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) [1] nats(N) -> cons(N, n__nats(s(N))) [1] zprimes -> sieve(nats(s(s(0)))) [1] filter(X1, X2, X3) -> n__filter(X1, X2, X3) [1] sieve(X) -> n__sieve(X) [1] nats(X) -> n__nats(X) [1] activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) [1] activate(n__sieve(X)) -> sieve(X) [1] activate(n__nats(X)) -> nats(X) [1] activate(X) -> X [1] The TRS has the following type information: filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats cons :: 0:s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0 :: 0:s n__filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats s :: 0:s -> 0:s sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats nats :: 0:s -> cons:n__filter:n__sieve:n__nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats 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: zprimes (c) The following functions are completely defined: nats_1 activate_1 filter_3 sieve_1 Due to the following rules being added: none And the following fresh constants: const ---------------------------------------- (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: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) [1] filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) [1] sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) [1] sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) [1] nats(N) -> cons(N, n__nats(s(N))) [1] zprimes -> sieve(nats(s(s(0)))) [1] filter(X1, X2, X3) -> n__filter(X1, X2, X3) [1] sieve(X) -> n__sieve(X) [1] nats(X) -> n__nats(X) [1] activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) [1] activate(n__sieve(X)) -> sieve(X) [1] activate(n__nats(X)) -> nats(X) [1] activate(X) -> X [1] The TRS has the following type information: filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats cons :: 0:s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0 :: 0:s n__filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats s :: 0:s -> 0:s sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats nats :: 0:s -> cons:n__filter:n__sieve:n__nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats const :: cons:n__filter:n__sieve:n__nats 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: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) [1] filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) [1] sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) [1] sieve(cons(s(N), n__filter(X1', X2', X3'))) -> cons(s(N), n__sieve(filter(filter(X1', X2', X3'), N, N))) [2] sieve(cons(s(N), n__sieve(X'))) -> cons(s(N), n__sieve(filter(sieve(X'), N, N))) [2] sieve(cons(s(N), n__nats(X''))) -> cons(s(N), n__sieve(filter(nats(X''), N, N))) [2] sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(Y, N, N))) [2] nats(N) -> cons(N, n__nats(s(N))) [1] zprimes -> sieve(cons(s(s(0)), n__nats(s(s(s(0)))))) [2] zprimes -> sieve(n__nats(s(s(0)))) [2] filter(X1, X2, X3) -> n__filter(X1, X2, X3) [1] sieve(X) -> n__sieve(X) [1] nats(X) -> n__nats(X) [1] activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) [1] activate(n__sieve(X)) -> sieve(X) [1] activate(n__nats(X)) -> nats(X) [1] activate(X) -> X [1] The TRS has the following type information: filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats cons :: 0:s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0 :: 0:s n__filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats s :: 0:s -> 0:s sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats nats :: 0:s -> cons:n__filter:n__sieve:n__nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats const :: cons:n__filter:n__sieve:n__nats 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: 0 => 0 const => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> sieve(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> nats(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> filter(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 filter(z, z', z'') -{ 1 }-> 1 + X + (1 + activate(Y) + N + M) :|: z' = 1 + N, Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z'' = M, N >= 0 filter(z, z', z'') -{ 1 }-> 1 + 0 + (1 + activate(Y) + M + M) :|: Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z' = 0, z'' = M filter(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 nats(z) -{ 1 }-> 1 + X :|: X >= 0, z = X nats(z) -{ 1 }-> 1 + N + (1 + (1 + N)) :|: z = N, N >= 0 sieve(z) -{ 1 }-> 1 + X :|: X >= 0, z = X sieve(z) -{ 1 }-> 1 + 0 + (1 + activate(Y)) :|: Y >= 0, z = 1 + 0 + Y sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(Y, N, N)) :|: Y >= 0, z = 1 + (1 + N) + Y, N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(sieve(X'), N, N)) :|: X' >= 0, z = 1 + (1 + N) + (1 + X'), N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(nats(X''), N, N)) :|: z = 1 + (1 + N) + (1 + X''), X'' >= 0, N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(filter(X1', X2', X3'), N, N)) :|: z = 1 + (1 + N) + (1 + X1' + X2' + X3'), X3' >= 0, X2' >= 0, X1' >= 0, N >= 0 zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0))) :|: zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: ---------------------------------------- (27) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: nats(z) -{ 1 }-> 1 + X :|: X >= 0, z = X nats(z) -{ 1 }-> 1 + N + (1 + (1 + N)) :|: z = N, N >= 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> sieve(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> filter(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X' activate(z) -{ 2 }-> 1 + N + (1 + (1 + N)) :|: z = 1 + X, X >= 0, X = N, N >= 0 filter(z, z', z'') -{ 1 }-> 1 + X + (1 + activate(Y) + N + M) :|: z' = 1 + N, Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z'' = M, N >= 0 filter(z, z', z'') -{ 1 }-> 1 + 0 + (1 + activate(Y) + M + M) :|: Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z' = 0, z'' = M filter(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 nats(z) -{ 1 }-> 1 + X :|: X >= 0, z = X nats(z) -{ 1 }-> 1 + N + (1 + (1 + N)) :|: z = N, N >= 0 sieve(z) -{ 1 }-> 1 + X :|: X >= 0, z = X sieve(z) -{ 1 }-> 1 + 0 + (1 + activate(Y)) :|: Y >= 0, z = 1 + 0 + Y sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(Y, N, N)) :|: Y >= 0, z = 1 + (1 + N) + Y, N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(sieve(X'), N, N)) :|: X' >= 0, z = 1 + (1 + N) + (1 + X'), N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(filter(X1', X2', X3'), N, N)) :|: z = 1 + (1 + N) + (1 + X1' + X2' + X3'), X3' >= 0, X2' >= 0, X1' >= 0, N >= 0 sieve(z) -{ 3 }-> 1 + (1 + N) + (1 + filter(1 + X, N, N)) :|: z = 1 + (1 + N) + (1 + X''), X'' >= 0, N >= 0, X >= 0, X'' = X sieve(z) -{ 3 }-> 1 + (1 + N) + (1 + filter(1 + N' + (1 + (1 + N')), N, N)) :|: z = 1 + (1 + N) + (1 + X''), X'' >= 0, N >= 0, X'' = N', N' >= 0 zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0))) :|: zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 1 }-> sieve(z - 1) :|: z - 1 >= 0 activate(z) -{ 1 }-> filter(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> 1 + N + (1 + (1 + N)) :|: z - 1 >= 0, z - 1 = N, N >= 0 filter(z, z', z'') -{ 1 }-> 1 + X + (1 + activate(Y) + (z' - 1) + z'') :|: Y >= 0, z = 1 + X + Y, X >= 0, z'' >= 0, z' - 1 >= 0 filter(z, z', z'') -{ 1 }-> 1 + 0 + (1 + activate(Y) + z'' + z'') :|: Y >= 0, z = 1 + X + Y, X >= 0, z'' >= 0, z' = 0 filter(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 nats(z) -{ 1 }-> 1 + z :|: z >= 0 nats(z) -{ 1 }-> 1 + z + (1 + (1 + z)) :|: z >= 0 sieve(z) -{ 1 }-> 1 + z :|: z >= 0 sieve(z) -{ 1 }-> 1 + 0 + (1 + activate(z - 1)) :|: z - 1 >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(Y, N, N)) :|: Y >= 0, z = 1 + (1 + N) + Y, N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(sieve(X'), N, N)) :|: X' >= 0, z = 1 + (1 + N) + (1 + X'), N >= 0 sieve(z) -{ 2 }-> 1 + (1 + N) + (1 + filter(filter(X1', X2', X3'), N, N)) :|: z = 1 + (1 + N) + (1 + X1' + X2' + X3'), X3' >= 0, X2' >= 0, X1' >= 0, N >= 0 sieve(z) -{ 3 }-> 1 + (1 + N) + (1 + filter(1 + X, N, N)) :|: z = 1 + (1 + N) + (1 + X''), X'' >= 0, N >= 0, X >= 0, X'' = X sieve(z) -{ 3 }-> 1 + (1 + N) + (1 + filter(1 + N' + (1 + (1 + N')), N, N)) :|: z = 1 + (1 + N) + (1 + X''), X'' >= 0, N >= 0, X'' = N', N' >= 0 zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0))) :|: zprimes -{ 2 }-> sieve(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: ---------------------------------------- (31) 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: none And the following fresh constants: const ---------------------------------------- (32) 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: filter(cons(X, Y), 0, M) -> cons(0, n__filter(activate(Y), M, M)) [1] filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) [1] sieve(cons(0, Y)) -> cons(0, n__sieve(activate(Y))) [1] sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) [1] nats(N) -> cons(N, n__nats(s(N))) [1] zprimes -> sieve(nats(s(s(0)))) [1] filter(X1, X2, X3) -> n__filter(X1, X2, X3) [1] sieve(X) -> n__sieve(X) [1] nats(X) -> n__nats(X) [1] activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) [1] activate(n__sieve(X)) -> sieve(X) [1] activate(n__nats(X)) -> nats(X) [1] activate(X) -> X [1] The TRS has the following type information: filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats cons :: 0:s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0 :: 0:s n__filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats s :: 0:s -> 0:s sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats nats :: 0:s -> cons:n__filter:n__sieve:n__nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats zprimes :: cons:n__filter:n__sieve:n__nats const :: cons:n__filter:n__sieve:n__nats Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 const => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> sieve(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> nats(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> filter(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 filter(z, z', z'') -{ 1 }-> 1 + X + (1 + activate(Y) + N + M) :|: z' = 1 + N, Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z'' = M, N >= 0 filter(z, z', z'') -{ 1 }-> 1 + 0 + (1 + activate(Y) + M + M) :|: Y >= 0, z = 1 + X + Y, X >= 0, M >= 0, z' = 0, z'' = M filter(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 nats(z) -{ 1 }-> 1 + X :|: X >= 0, z = X nats(z) -{ 1 }-> 1 + N + (1 + (1 + N)) :|: z = N, N >= 0 sieve(z) -{ 1 }-> 1 + X :|: X >= 0, z = X sieve(z) -{ 1 }-> 1 + 0 + (1 + activate(Y)) :|: Y >= 0, z = 1 + 0 + Y sieve(z) -{ 1 }-> 1 + (1 + N) + (1 + filter(activate(Y), N, N)) :|: Y >= 0, z = 1 + (1 + N) + Y, N >= 0 zprimes -{ 1 }-> sieve(nats(1 + (1 + 0))) :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) FILTER(z0, z1, z2) -> c2 SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) SIEVE(z0) -> c5 NATS(z0) -> c6 NATS(z0) -> c7 ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) ACTIVATE(z0) -> c12 K tuples:none Defined Rule Symbols: filter_3, sieve_1, nats_1, zprimes, activate_1 Defined Pair Symbols: FILTER_3, SIEVE_1, NATS_1, ZPRIMES, ACTIVATE_1 Compound Symbols: c_1, c1_1, c2, c3_1, c4_2, c5, c6, c7, c8_2, c9_1, c10_1, c11_1, c12 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) SIEVE(z0) -> c5 FILTER(z0, z1, z2) -> c2 ACTIVATE(z0) -> c12 NATS(z0) -> c7 NATS(z0) -> c6 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ZPRIMES -> c8(SIEVE(nats(s(s(0)))), NATS(s(s(0)))) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) K tuples:none Defined Rule Symbols: filter_3, sieve_1, nats_1, zprimes, activate_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ZPRIMES, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c4_2, c8_2, c9_1, c10_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) K tuples:none Defined Rule Symbols: filter_3, sieve_1, nats_1, zprimes, activate_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c4_2, c9_1, c10_1, c8_1 ---------------------------------------- (41) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) zprimes -> sieve(nats(s(s(0)))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) K tuples: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) Defined Rule Symbols: filter_3, sieve_1, nats_1, zprimes, activate_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c4_2, c9_1, c10_1, c8_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: zprimes -> sieve(nats(s(s(0)))) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) K tuples: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c4_2, c9_1, c10_1, c8_1 ---------------------------------------- (45) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (46) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) The (relative) TRS S consists of the following rules: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (47) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (48) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (49) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (50) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) [1] FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) [1] SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) [1] ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) [1] ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) [1] ZPRIMES -> c8(SIEVE(nats(s(s(0))))) [0] activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) [0] activate(n__sieve(z0)) -> sieve(z0) [0] activate(n__nats(z0)) -> nats(z0) [0] activate(z0) -> z0 [0] filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) [0] filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) [0] filter(z0, z1, z2) -> n__filter(z0, z1, z2) [0] sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) [0] sieve(z0) -> n__sieve(z0) [0] nats(z0) -> cons(z0, n__nats(s(z0))) [0] nats(z0) -> n__nats(z0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (51) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) [1] FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) [1] SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) [1] ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) [1] ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) [1] ZPRIMES -> c8(SIEVE(nats(s(s(0))))) [0] activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) [0] activate(n__sieve(z0)) -> sieve(z0) [0] activate(n__nats(z0)) -> nats(z0) [0] activate(z0) -> z0 [0] filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) [0] filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) [0] filter(z0, z1, z2) -> n__filter(z0, z1, z2) [0] sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) [0] sieve(z0) -> n__sieve(z0) [0] nats(z0) -> cons(z0, n__nats(s(z0))) [0] nats(z0) -> n__nats(z0) [0] The TRS has the following type information: FILTER :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> c:c1 cons :: 0:s -> cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats 0 :: 0:s c :: c9:c10 -> c:c1 ACTIVATE :: cons:n__filter:n__sieve:n__nats -> c9:c10 s :: 0:s -> 0:s c1 :: c9:c10 -> c:c1 SIEVE :: cons:n__filter:n__sieve:n__nats -> c3:c4 c3 :: c9:c10 -> c3:c4 c4 :: c:c1 -> c9:c10 -> c3:c4 activate :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats c9 :: c:c1 -> c9:c10 n__sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats c10 :: c3:c4 -> c9:c10 ZPRIMES :: c8 c8 :: c3:c4 -> c8 nats :: 0:s -> cons:n__filter:n__sieve:n__nats filter :: cons:n__filter:n__sieve:n__nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats sieve :: cons:n__filter:n__sieve:n__nats -> cons:n__filter:n__sieve:n__nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats Rewrite Strategy: INNERMOST ---------------------------------------- (53) 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: FILTER_3 SIEVE_1 ACTIVATE_1 (c) The following functions are completely defined: ZPRIMES activate_1 filter_3 sieve_1 nats_1 Due to the following rules being added: ZPRIMES -> const4 [0] activate(v0) -> const1 [0] filter(v0, v1, v2) -> const1 [0] sieve(v0) -> const1 [0] nats(v0) -> const1 [0] And the following fresh constants: const4, const1, const, const2, const3 ---------------------------------------- (54) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) [1] FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) [1] SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) [1] ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) [1] ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) [1] ZPRIMES -> c8(SIEVE(nats(s(s(0))))) [0] activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) [0] activate(n__sieve(z0)) -> sieve(z0) [0] activate(n__nats(z0)) -> nats(z0) [0] activate(z0) -> z0 [0] filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) [0] filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) [0] filter(z0, z1, z2) -> n__filter(z0, z1, z2) [0] sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) [0] sieve(z0) -> n__sieve(z0) [0] nats(z0) -> cons(z0, n__nats(s(z0))) [0] nats(z0) -> n__nats(z0) [0] ZPRIMES -> const4 [0] activate(v0) -> const1 [0] filter(v0, v1, v2) -> const1 [0] sieve(v0) -> const1 [0] nats(v0) -> const1 [0] The TRS has the following type information: FILTER :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> c:c1 cons :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 0 :: 0:s c :: c9:c10 -> c:c1 ACTIVATE :: cons:n__filter:n__sieve:n__nats:const1 -> c9:c10 s :: 0:s -> 0:s c1 :: c9:c10 -> c:c1 SIEVE :: cons:n__filter:n__sieve:n__nats:const1 -> c3:c4 c3 :: c9:c10 -> c3:c4 c4 :: c:c1 -> c9:c10 -> c3:c4 activate :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 n__filter :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:const1 c9 :: c:c1 -> c9:c10 n__sieve :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 c10 :: c3:c4 -> c9:c10 ZPRIMES :: c8:const4 c8 :: c3:c4 -> c8:const4 nats :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 filter :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:const1 sieve :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 const4 :: c8:const4 const1 :: cons:n__filter:n__sieve:n__nats:const1 const :: c:c1 const2 :: c9:c10 const3 :: c3:c4 Rewrite Strategy: INNERMOST ---------------------------------------- (55) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (56) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) [1] FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) [1] SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) [1] SIEVE(cons(s(z0), n__filter(z0', z1', z2'))) -> c4(FILTER(filter(z0', z1', z2'), z0, z0), ACTIVATE(n__filter(z0', z1', z2'))) [1] SIEVE(cons(s(z0), n__sieve(z0''))) -> c4(FILTER(sieve(z0''), z0, z0), ACTIVATE(n__sieve(z0''))) [1] SIEVE(cons(s(z0), n__nats(z01))) -> c4(FILTER(nats(z01), z0, z0), ACTIVATE(n__nats(z01))) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(z1, z0, z0), ACTIVATE(z1)) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(const1, z0, z0), ACTIVATE(z1)) [1] ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) [1] ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) [1] ZPRIMES -> c8(SIEVE(cons(s(s(0)), n__nats(s(s(s(0))))))) [0] ZPRIMES -> c8(SIEVE(n__nats(s(s(0))))) [0] ZPRIMES -> c8(SIEVE(const1)) [0] activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) [0] activate(n__sieve(z0)) -> sieve(z0) [0] activate(n__nats(z0)) -> nats(z0) [0] activate(z0) -> z0 [0] filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) [0] filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) [0] filter(z0, z1, z2) -> n__filter(z0, z1, z2) [0] sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) [0] sieve(cons(s(z0), n__filter(z02, z1'', z2''))) -> cons(s(z0), n__sieve(filter(filter(z02, z1'', z2''), z0, z0))) [0] sieve(cons(s(z0), n__sieve(z03))) -> cons(s(z0), n__sieve(filter(sieve(z03), z0, z0))) [0] sieve(cons(s(z0), n__nats(z04))) -> cons(s(z0), n__sieve(filter(nats(z04), z0, z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(z1, z0, z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(const1, z0, z0))) [0] sieve(z0) -> n__sieve(z0) [0] nats(z0) -> cons(z0, n__nats(s(z0))) [0] nats(z0) -> n__nats(z0) [0] ZPRIMES -> const4 [0] activate(v0) -> const1 [0] filter(v0, v1, v2) -> const1 [0] sieve(v0) -> const1 [0] nats(v0) -> const1 [0] The TRS has the following type information: FILTER :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> c:c1 cons :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 0 :: 0:s c :: c9:c10 -> c:c1 ACTIVATE :: cons:n__filter:n__sieve:n__nats:const1 -> c9:c10 s :: 0:s -> 0:s c1 :: c9:c10 -> c:c1 SIEVE :: cons:n__filter:n__sieve:n__nats:const1 -> c3:c4 c3 :: c9:c10 -> c3:c4 c4 :: c:c1 -> c9:c10 -> c3:c4 activate :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 n__filter :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:const1 c9 :: c:c1 -> c9:c10 n__sieve :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 c10 :: c3:c4 -> c9:c10 ZPRIMES :: c8:const4 c8 :: c3:c4 -> c8:const4 nats :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 filter :: cons:n__filter:n__sieve:n__nats:const1 -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:const1 sieve :: cons:n__filter:n__sieve:n__nats:const1 -> cons:n__filter:n__sieve:n__nats:const1 n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats:const1 const4 :: c8:const4 const1 :: cons:n__filter:n__sieve:n__nats:const1 const :: c:c1 const2 :: c9:c10 const3 :: c3:c4 Rewrite Strategy: INNERMOST ---------------------------------------- (57) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 const4 => 0 const1 => 0 const => 0 const2 => 0 const3 => 0 ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + SIEVE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + FILTER(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 SIEVE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z0 >= 0, z = 1 + 0 + z0 SIEVE(z) -{ 1 }-> 1 + FILTER(z1, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(sieve(z0''), z0, z0) + ACTIVATE(1 + z0'') :|: z = 1 + (1 + z0) + (1 + z0''), z0 >= 0, z0'' >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(nats(z01), z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(filter(z0', z1', z2'), z0, z0) + ACTIVATE(1 + z0' + z1' + z2') :|: z = 1 + (1 + z0) + (1 + z0' + z1' + z2'), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(0, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 ZPRIMES -{ 0 }-> 0 :|: ZPRIMES -{ 0 }-> 1 + SIEVE(0) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0))) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> sieve(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> nats(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> filter(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 filter(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + (1 + activate(z1) + z2 + z3) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 filter(z, z', z'') -{ 0 }-> 1 + 0 + (1 + activate(z1) + z2 + z2) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 nats(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 nats(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 nats(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 sieve(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 1 + 0 + (1 + activate(z0)) :|: z0 >= 0, z = 1 + 0 + z0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(z1, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(sieve(z03), z0, z0)) :|: z0 >= 0, z03 >= 0, z = 1 + (1 + z0) + (1 + z03) sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(nats(z04), z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04) sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(filter(z02, z1'', z2''), z0, z0)) :|: z = 1 + (1 + z0) + (1 + z02 + z1'' + z2''), z02 >= 0, z0 >= 0, z2'' >= 0, z1'' >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(0, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 ---------------------------------------- (59) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: nats(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0 nats(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 nats(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + SIEVE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + FILTER(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 SIEVE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z0 >= 0, z = 1 + 0 + z0 SIEVE(z) -{ 1 }-> 1 + FILTER(z1, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(sieve(z0''), z0, z0) + ACTIVATE(1 + z0'') :|: z = 1 + (1 + z0) + (1 + z0''), z0 >= 0, z0'' >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(filter(z0', z1', z2'), z0, z0) + ACTIVATE(1 + z0' + z1' + z2') :|: z = 1 + (1 + z0) + (1 + z0' + z1' + z2'), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(0, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(0, z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, v0 >= 0, z01 = v0 SIEVE(z) -{ 1 }-> 1 + FILTER(1 + z0', z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, z01 = z0', z0' >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(1 + z0' + (1 + (1 + z0')), z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, z01 = z0', z0' >= 0 ZPRIMES -{ 0 }-> 0 :|: ZPRIMES -{ 0 }-> 1 + SIEVE(0) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0))) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> sieve(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> filter(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, z0 = v0 activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0 filter(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + (1 + activate(z1) + z2 + z3) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 filter(z, z', z'') -{ 0 }-> 1 + 0 + (1 + activate(z1) + z2 + z2) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 nats(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 nats(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 nats(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 sieve(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 1 + 0 + (1 + activate(z0)) :|: z0 >= 0, z = 1 + 0 + z0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(z1, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(sieve(z03), z0, z0)) :|: z0 >= 0, z03 >= 0, z = 1 + (1 + z0) + (1 + z03) sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(filter(z02, z1'', z2''), z0, z0)) :|: z = 1 + (1 + z0) + (1 + z02 + z1'' + z2''), z02 >= 0, z0 >= 0, z2'' >= 0, z1'' >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(0, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(0, z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), v0 >= 0, z04 = v0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(1 + z0', z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), z04 = z0', z0' >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(1 + z0' + (1 + (1 + z0')), z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), z04 = z0', z0' >= 0 ---------------------------------------- (61) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 1 }-> 1 + SIEVE(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + FILTER(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z'' >= 0, z' = 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' - 1 >= 0, z'' >= 0 SIEVE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(z1, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(sieve(z0''), z0, z0) + ACTIVATE(1 + z0'') :|: z = 1 + (1 + z0) + (1 + z0''), z0 >= 0, z0'' >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(filter(z0', z1', z2'), z0, z0) + ACTIVATE(1 + z0' + z1' + z2') :|: z = 1 + (1 + z0) + (1 + z0' + z1' + z2'), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(0, z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(0, z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, v0 >= 0, z01 = v0 SIEVE(z) -{ 1 }-> 1 + FILTER(1 + z0', z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, z01 = z0', z0' >= 0 SIEVE(z) -{ 1 }-> 1 + FILTER(1 + z0' + (1 + (1 + z0')), z0, z0) + ACTIVATE(1 + z01) :|: z01 >= 0, z = 1 + (1 + z0) + (1 + z01), z0 >= 0, z01 = z0', z0' >= 0 ZPRIMES -{ 0 }-> 0 :|: ZPRIMES -{ 0 }-> 1 + SIEVE(0) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0))) :|: ZPRIMES -{ 0 }-> 1 + SIEVE(1 + (1 + (1 + 0)) + (1 + (1 + (1 + (1 + 0))))) :|: activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> sieve(z - 1) :|: z - 1 >= 0 activate(z) -{ 0 }-> filter(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0 activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0 activate(z) -{ 0 }-> 1 + z0' + (1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0 filter(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + (1 + activate(z1) + (z' - 1) + z'') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' - 1 >= 0, z'' >= 0 filter(z, z', z'') -{ 0 }-> 1 + 0 + (1 + activate(z1) + z'' + z'') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z'' >= 0, z' = 0 filter(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 nats(z) -{ 0 }-> 0 :|: z >= 0 nats(z) -{ 0 }-> 1 + z :|: z >= 0 nats(z) -{ 0 }-> 1 + z + (1 + (1 + z)) :|: z >= 0 sieve(z) -{ 0 }-> 0 :|: z >= 0 sieve(z) -{ 0 }-> 1 + z :|: z >= 0 sieve(z) -{ 0 }-> 1 + 0 + (1 + activate(z - 1)) :|: z - 1 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(z1, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(sieve(z03), z0, z0)) :|: z0 >= 0, z03 >= 0, z = 1 + (1 + z0) + (1 + z03) sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(filter(z02, z1'', z2''), z0, z0)) :|: z = 1 + (1 + z0) + (1 + z02 + z1'' + z2''), z02 >= 0, z0 >= 0, z2'' >= 0, z1'' >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(0, z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(0, z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), v0 >= 0, z04 = v0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(1 + z0', z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), z04 = z0', z0' >= 0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(1 + z0' + (1 + (1 + z0')), z0, z0)) :|: z04 >= 0, z0 >= 0, z = 1 + (1 + z0) + (1 + z04), z04 = z0', z0' >= 0 ---------------------------------------- (63) 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: ZPRIMES -> null_ZPRIMES [0] activate(v0) -> null_activate [0] filter(v0, v1, v2) -> null_filter [0] sieve(v0) -> null_sieve [0] nats(v0) -> null_nats [0] FILTER(v0, v1, v2) -> null_FILTER [0] SIEVE(v0) -> null_SIEVE [0] ACTIVATE(v0) -> null_ACTIVATE [0] And the following fresh constants: null_ZPRIMES, null_activate, null_filter, null_sieve, null_nats, null_FILTER, null_SIEVE, null_ACTIVATE ---------------------------------------- (64) 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: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) [1] FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) [1] SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) [1] SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) [1] ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) [1] ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) [1] ZPRIMES -> c8(SIEVE(nats(s(s(0))))) [0] activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) [0] activate(n__sieve(z0)) -> sieve(z0) [0] activate(n__nats(z0)) -> nats(z0) [0] activate(z0) -> z0 [0] filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) [0] filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) [0] filter(z0, z1, z2) -> n__filter(z0, z1, z2) [0] sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) [0] sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) [0] sieve(z0) -> n__sieve(z0) [0] nats(z0) -> cons(z0, n__nats(s(z0))) [0] nats(z0) -> n__nats(z0) [0] ZPRIMES -> null_ZPRIMES [0] activate(v0) -> null_activate [0] filter(v0, v1, v2) -> null_filter [0] sieve(v0) -> null_sieve [0] nats(v0) -> null_nats [0] FILTER(v0, v1, v2) -> null_FILTER [0] SIEVE(v0) -> null_SIEVE [0] ACTIVATE(v0) -> null_ACTIVATE [0] The TRS has the following type information: FILTER :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> 0:s -> 0:s -> c:c1:null_FILTER cons :: 0:s -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats 0 :: 0:s c :: c9:c10:null_ACTIVATE -> c:c1:null_FILTER ACTIVATE :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> c9:c10:null_ACTIVATE s :: 0:s -> 0:s c1 :: c9:c10:null_ACTIVATE -> c:c1:null_FILTER SIEVE :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> c3:c4:null_SIEVE c3 :: c9:c10:null_ACTIVATE -> c3:c4:null_SIEVE c4 :: c:c1:null_FILTER -> c9:c10:null_ACTIVATE -> c3:c4:null_SIEVE activate :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats n__filter :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats c9 :: c:c1:null_FILTER -> c9:c10:null_ACTIVATE n__sieve :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats c10 :: c3:c4:null_SIEVE -> c9:c10:null_ACTIVATE ZPRIMES :: c8:null_ZPRIMES c8 :: c3:c4:null_SIEVE -> c8:null_ZPRIMES nats :: 0:s -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats filter :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> 0:s -> 0:s -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats sieve :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats n__nats :: 0:s -> cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats null_ZPRIMES :: c8:null_ZPRIMES null_activate :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats null_filter :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats null_sieve :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats null_nats :: cons:n__filter:n__sieve:n__nats:null_activate:null_filter:null_sieve:null_nats null_FILTER :: c:c1:null_FILTER null_SIEVE :: c3:c4:null_SIEVE null_ACTIVATE :: c9:c10:null_ACTIVATE Rewrite Strategy: INNERMOST ---------------------------------------- (65) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_ZPRIMES => 0 null_activate => 0 null_filter => 0 null_sieve => 0 null_nats => 0 null_FILTER => 0 null_SIEVE => 0 null_ACTIVATE => 0 ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ACTIVATE(z) -{ 1 }-> 1 + SIEVE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + FILTER(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 FILTER(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 FILTER(z, z', z'') -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 SIEVE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 SIEVE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z0 >= 0, z = 1 + 0 + z0 SIEVE(z) -{ 1 }-> 1 + FILTER(activate(z1), z0, z0) + ACTIVATE(z1) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 ZPRIMES -{ 0 }-> 0 :|: ZPRIMES -{ 0 }-> 1 + SIEVE(nats(1 + (1 + 0))) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> sieve(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> nats(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> filter(z0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 filter(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + (1 + activate(z1) + z2 + z3) :|: z1 >= 0, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z' = 1 + z2, z2 >= 0, z3 >= 0 filter(z, z', z'') -{ 0 }-> 1 + 0 + (1 + activate(z1) + z2 + z2) :|: z'' = z2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z' = 0 filter(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 nats(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 nats(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 nats(z) -{ 0 }-> 1 + z0 + (1 + (1 + z0)) :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 sieve(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 sieve(z) -{ 0 }-> 1 + 0 + (1 + activate(z0)) :|: z0 >= 0, z = 1 + 0 + z0 sieve(z) -{ 0 }-> 1 + (1 + z0) + (1 + filter(activate(z1), z0, z0)) :|: z1 >= 0, z = 1 + (1 + z0) + z1, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SIEVE(cons(s(z0), z1)) -> c4(FILTER(activate(z1), z0, z0), ACTIVATE(z1)) by SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0), ACTIVATE(n__nats(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0), ACTIVATE(n__nats(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0), ACTIVATE(n__nats(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) K tuples: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c8_1, c4_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) ZPRIMES -> c8(SIEVE(nats(s(s(0))))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) K tuples: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c8_1, c4_2, c4_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZPRIMES -> c8(SIEVE(nats(s(s(0))))) by ZPRIMES -> c8(SIEVE(cons(s(s(0)), n__nats(s(s(s(0))))))) ZPRIMES -> c8(SIEVE(n__nats(s(s(0))))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) ZPRIMES -> c8(SIEVE(cons(s(s(0)), n__nats(s(s(s(0))))))) ZPRIMES -> c8(SIEVE(n__nats(s(s(0))))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) K tuples: ZPRIMES -> c8(SIEVE(nats(s(s(0))))) Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1, ZPRIMES Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1, c8_1 ---------------------------------------- (73) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ZPRIMES -> c8(SIEVE(cons(s(s(0)), n__nats(s(s(s(0))))))) Removed 1 trailing nodes: ZPRIMES -> c8(SIEVE(n__nats(s(s(0))))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) by SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(n__filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(n__filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(FILTER(n__filter(z0, z1, z2), x0, x0), ACTIVATE(n__filter(z0, z1, z2))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) by SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(n__sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(n__sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(FILTER(n__sieve(z0), x0, x0), ACTIVATE(n__sieve(z0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(nats(z0), x0, x0)) by SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(n__nats(z0), x0, x0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(n__nats(z0), x0, x0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(n__nats(z0), x0, x0)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(n__nats(z0), x0, x0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) S tuples: FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c_1, c1_1, c3_1, c9_1, c10_1, c4_2, c4_1 ---------------------------------------- (87) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, z1), 0, z2) -> c(ACTIVATE(z1)) by FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) S tuples: FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: FILTER_3, SIEVE_1, ACTIVATE_1 Compound Symbols: c1_1, c3_1, c9_1, c10_1, c4_2, c4_1, c_1 ---------------------------------------- (89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, z1), s(z2), z3) -> c1(ACTIVATE(z1)) by FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) S tuples: SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c3_1, c9_1, c10_1, c4_2, c4_1, c_1, c1_1 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(cons(z0, n__nats(s(z0))), x0, x0)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) S tuples: SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c3_1, c9_1, c10_1, c4_2, c4_1, c_1, c1_1 ---------------------------------------- (93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(0, z0)) -> c3(ACTIVATE(z0)) by SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) S tuples: ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: ACTIVATE_1, SIEVE_1, FILTER_3 Compound Symbols: c9_1, c10_1, c4_2, c4_1, c_1, c1_1, c3_1 ---------------------------------------- (95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__filter(z0, z1, z2)) -> c9(FILTER(z0, z1, z2)) by ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) S tuples: ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: ACTIVATE_1, SIEVE_1, FILTER_3 Compound Symbols: c10_1, c4_2, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(z0)) -> c10(SIEVE(z0)) by ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) S tuples: SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c_1, c1_1, c3_1, c9_1, c10_1 ---------------------------------------- (99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(x0), z0)) -> c4(FILTER(z0, x0, x0), ACTIVATE(z0)) by SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4)), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2)), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), 0, y2), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), s(y2), y3), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(FILTER(n__sieve(cons(s(y0), y1)), z0, z0), ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(y1, y2, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(y1))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(FILTER(n__sieve(cons(0, n__filter(y0, y1, y2))), z0, z0), ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(FILTER(n__sieve(cons(0, n__sieve(y0))), z0, z0), ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4)), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2)), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), 0, y2), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), s(y2), y3), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(FILTER(n__sieve(cons(s(y0), y1)), z0, z0), ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(y1, y2, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(y1))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(FILTER(n__sieve(cons(0, n__filter(y0, y1, y2))), z0, z0), ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(FILTER(n__sieve(cons(0, n__sieve(y0))), z0, z0), ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4)), ACTIVATE(cons(y0, n__filter(y1, y2, y3)))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2)), ACTIVATE(cons(y0, n__sieve(y1)))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), 0, y2), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(FILTER(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5), z0, z0), ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(FILTER(n__filter(cons(y0, n__sieve(y1)), s(y2), y3), z0, z0), ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(FILTER(n__sieve(cons(s(y0), y1)), z0, z0), ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(FILTER(n__sieve(cons(s(y0), n__filter(y1, y2, y3))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(FILTER(n__sieve(cons(s(y0), n__sieve(y1))), z0, z0), ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(FILTER(n__sieve(cons(0, n__filter(y0, y1, y2))), z0, z0), ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(FILTER(n__sieve(cons(0, n__sieve(y0))), z0, z0), ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c_1, c1_1, c3_1, c9_1, c10_1 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c_1, c1_1, c3_1, c9_1, c10_1 ---------------------------------------- (103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(x0), n__filter(z0, z1, z2))) -> c4(ACTIVATE(n__filter(z0, z1, z2))) by SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c_1, c1_1, c3_1, c9_1, c10_1 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(x0), n__sieve(z0))) -> c4(ACTIVATE(n__sieve(z0))) by SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c_1, c1_1, c3_1, c9_1, c10_1, c4_1 ---------------------------------------- (107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, n__filter(y0, y1, y2)), 0, z2) -> c(ACTIVATE(n__filter(y0, y1, y2))) by FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c_1, c1_1, c3_1, c9_1, c10_1, c4_1 ---------------------------------------- (109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, n__sieve(y0)), 0, z2) -> c(ACTIVATE(n__sieve(y0))) by FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c1_1, c3_1, c9_1, c10_1, c4_1, c_1 ---------------------------------------- (111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, n__filter(y0, y1, y2)), s(z2), z3) -> c1(ACTIVATE(n__filter(y0, y1, y2))) by FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, FILTER_3, ACTIVATE_1 Compound Symbols: c4_2, c1_1, c3_1, c9_1, c10_1, c4_1, c_1 ---------------------------------------- (113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace FILTER(cons(z0, n__sieve(y0)), s(z2), z3) -> c1(ACTIVATE(n__sieve(y0))) by FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c3_1, c9_1, c10_1, c4_1, c_1, c1_1 ---------------------------------------- (115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(0, n__filter(y0, y1, y2))) -> c3(ACTIVATE(n__filter(y0, y1, y2))) by SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c3_1, c9_1, c10_1, c4_1, c_1, c1_1 ---------------------------------------- (117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(0, n__sieve(y0))) -> c3(ACTIVATE(n__sieve(y0))) by SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c9_1, c10_1, c4_1, c_1, c1_1, c3_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, z2)) by ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c9_1, c10_1, c4_1, c_1, c1_1, c3_1 ---------------------------------------- (121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), 0, z2)) by ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c9_1, c10_1, c4_1, c_1, c1_1, c3_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) -> c9(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)) by ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c9_1, c10_1, c4_1, c_1, c1_1, c3_1 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2)) -> c9(FILTER(cons(y0, n__sieve(y1)), s(y2), z2)) by ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(cons(s(y0), y1))) -> c10(SIEVE(cons(s(y0), y1))) by ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(y1, y2, y3)))) by ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, y2), 0, z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, y2), 0, z3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, y2), s(y3), z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, y2), s(y3), z3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, z3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1)))) -> c10(SIEVE(cons(s(y0), n__sieve(y1)))) by ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2)))) -> c10(SIEVE(cons(0, n__filter(y0, y1, y2)))) by ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__sieve(cons(0, n__sieve(y0)))) -> c10(SIEVE(cons(0, n__sieve(y0)))) by ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), 0, 0)) by SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(0), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), 0, 0)) by SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(s(y4)), cons(y0, n__filter(y1, y2, y3)))) -> c4(FILTER(cons(y0, n__filter(y1, y2, y3)), s(y4), s(y4))) by SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(s(y2)), cons(y0, n__sieve(y1)))) -> c4(FILTER(cons(y0, n__sieve(y1)), s(y2), s(y2))) by SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (147) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (149) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (151) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (153) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (155) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), z4))))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (157) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (159) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) by SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (161) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) by SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, y4))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, y2))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, y2))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), 0, z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), y5))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), y3))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) -> c4(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) by SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), y1)))) -> c4(ACTIVATE(n__sieve(cons(s(y0), y1)))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, y2), s(y3), z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), z4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), z4))))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(y1))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) by SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) by SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__filter(z0, z1, z2)) -> filter(z0, z1, z2) activate(n__sieve(z0)) -> sieve(z0) activate(n__nats(z0)) -> nats(z0) activate(z0) -> z0 filter(cons(z0, z1), 0, z2) -> cons(0, n__filter(activate(z1), z2, z2)) filter(cons(z0, z1), s(z2), z3) -> cons(z0, n__filter(activate(z1), z2, z3)) filter(z0, z1, z2) -> n__filter(z0, z1, z2) sieve(cons(0, z0)) -> cons(0, n__sieve(activate(z0))) sieve(cons(s(z0), z1)) -> cons(s(z0), n__sieve(filter(activate(z1), z0, z0))) sieve(z0) -> n__sieve(z0) nats(z0) -> cons(z0, n__nats(s(z0))) nats(z0) -> n__nats(z0) Tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y0))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) S tuples: SIEVE(cons(s(x0), n__filter(cons(z0, z1), 0, z2))) -> c4(FILTER(cons(0, n__filter(activate(z1), z2, z2)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), 0, z2))) SIEVE(cons(s(x0), n__filter(cons(z0, z1), s(z2), z3))) -> c4(FILTER(cons(z0, n__filter(activate(z1), z2, z3)), x0, x0), ACTIVATE(n__filter(cons(z0, z1), s(z2), z3))) SIEVE(cons(s(x0), n__sieve(cons(0, z0)))) -> c4(FILTER(cons(0, n__sieve(activate(z0))), x0, x0), ACTIVATE(n__sieve(cons(0, z0)))) SIEVE(cons(s(x0), n__sieve(cons(s(z0), z1)))) -> c4(FILTER(cons(s(z0), n__sieve(filter(activate(z1), z0, z0))), x0, x0), ACTIVATE(n__sieve(cons(s(z0), z1)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))) ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) -> c10(SIEVE(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(0, y1))))) ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))) -> c10(SIEVE(cons(s(y0), n__sieve(cons(s(y1), y2))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), 0, z4) -> c(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), 0, z2) -> c(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), 0, z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z3))) FILTER(cons(z0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))) FILTER(cons(z0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3)), s(z4), z5) -> c1(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z3))) FILTER(cons(z0, n__sieve(cons(s(y0), y1))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), y1)))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) FILTER(cons(z0, n__sieve(cons(s(y0), n__sieve(y1)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) FILTER(cons(z0, n__sieve(cons(0, n__filter(y0, y1, y2)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) FILTER(cons(z0, n__sieve(cons(0, n__sieve(y0)))), s(z2), z3) -> c1(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), 0, z2))) SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2))) SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) -> c3(ACTIVATE(n__filter(cons(y0, n__sieve(y1)), s(y2), z2))) SIEVE(cons(0, n__sieve(cons(s(y0), y1)))) -> c3(ACTIVATE(n__sieve(cons(s(y0), y1)))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__filter(y1, y2, y3))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))) SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))) -> c3(ACTIVATE(n__sieve(cons(s(y0), n__sieve(y1))))) SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))) -> c3(ACTIVATE(n__sieve(cons(0, n__filter(y0, y1, y2))))) SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0))))) -> c3(ACTIVATE(n__sieve(cons(0, n__sieve(y0))))) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, z4)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, z2)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) -> c9(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), s(z4), z5)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z2), z3)) ACTIVATE(n__filter(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) -> c9(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), s(z2), z3)) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) -> c10(SIEVE(cons(s(0), cons(y0, n__filter(y1, y2, y3))))) ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1))))) -> c10(SIEVE(cons(s(0), cons(y0, n__sieve(y1))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4))))) ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2))))) -> c10(SIEVE(cons(s(s(y0)), cons(y1, n__sieve(y2))))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), 0, y3)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6)))) ACTIVATE(n__sieve(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) -> c10(SIEVE(cons(s(z0), n__filter(cons(y1, n__sieve(y2)), s(y3), y4)))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(s(y1), n__sieve(y2)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) -> c10(SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z2)))) ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) -> c10(SIEVE(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z2)))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), y1))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2))))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) -> c10(SIEVE(cons(0, n__sieve(cons(s(y0), n__sieve(y1)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2)))))) ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0)))))) -> c10(SIEVE(cons(0, n__sieve(cons(0, n__sieve(y0)))))) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), 0, z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)))) -> c4(FILTER(cons(z0, n__filter(cons(y1, n__sieve(y2)), s(y3), z3)), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), y2))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z0, n__sieve(cons(s(y1), n__sieve(y2)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, 0)) SIEVE(cons(s(0), cons(z0, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z0, n__sieve(cons(0, n__sieve(y1)))), 0, 0)) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)))) -> c4(FILTER(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), y2))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), y2))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))))) -> c4(FILTER(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z0), s(z0))) SIEVE(cons(s(s(z0)), cons(z1, n__sieve(cons(0, n__sieve(y1)))))) -> c4(FILTER(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z0), s(z0))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), 0, z5))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), 0, z3))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), 0, z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) -> c4(ACTIVATE(n__filter(cons(z1, n__filter(cons(y1, n__sieve(y2)), s(y3), z4)), s(z5), z6))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), y2))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__filter(y2, y3, y4)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(0, y2))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3))))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(s(y1), n__sieve(y2)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__filter(y1, y2, y3)))), s(z3), z4))) SIEVE(cons(s(z0), n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) -> c4(ACTIVATE(n__filter(cons(z1, n__sieve(cons(0, n__sieve(y1)))), s(z3), z4))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__filter(y1, y2, y3)))))) SIEVE(cons(s(z0), n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) -> c4(ACTIVATE(n__sieve(cons(s(0), cons(y0, n__sieve(y1)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__filter(y2, y3, y4)))))) SIEVE(cons(s(z0), n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) -> c4(ACTIVATE(n__sieve(cons(s(s(y0)), cons(y1, n__sieve(y2)))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), 0, y5))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), 0, y3))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__filter(y2, y3, y4)), s(y5), y6))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__filter(cons(y1, n__sieve(y2)), s(y3), y4))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), 0, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(cons(y2, y3), s(y4), y5))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__filter(y2, y3, y4))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(0, y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(cons(s(y2), y3)))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(s(y1), n__sieve(y2))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(s(z1), n__sieve(cons(0, n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), 0, z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__filter(y1, y2, y3)), s(y4), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) -> c4(ACTIVATE(n__sieve(cons(0, n__filter(cons(y0, n__sieve(y1)), s(y2), z3))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), y1)))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), 0, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(cons(y1, y2), s(y3), y4))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__filter(y1, y2, y3))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(0, y1)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(cons(s(y1), y2)))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(s(y0), n__sieve(y1))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__filter(y0, y1, y2))))))) SIEVE(cons(s(z0), n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) -> c4(ACTIVATE(n__sieve(cons(0, n__sieve(cons(0, n__sieve(y0))))))) K tuples:none Defined Rule Symbols: activate_1, filter_3, sieve_1, nats_1 Defined Pair Symbols: SIEVE_1, ACTIVATE_1, FILTER_3 Compound Symbols: c4_2, c10_1, c4_1, c_1, c1_1, c3_1, c9_1