KILLED proof of input_WIqfF1108H.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 113 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 5 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms] (64) CdtProblem (65) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 6 ms] (84) CdtProblem (85) CdtForwardInstantiationProof [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) CdtForwardInstantiationProof [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) CdtForwardInstantiationProof [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), 0 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 4 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), 4 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), 0 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (144) 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) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) 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 ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) 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 ---------------------------------------- (9) 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 ---------------------------------------- (10) 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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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 ---------------------------------------- (13) 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 ---------------------------------------- (14) 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))))) :|: ---------------------------------------- (15) 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 ---------------------------------------- (16) 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))))) :|: ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) 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))))) :|: ---------------------------------------- (19) 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 ---------------------------------------- (20) 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 ---------------------------------------- (21) 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 ---------------------------------------- (22) 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) 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 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: ACTIVATE(n__nats(z0)) -> c11(NATS(z0)) FILTER(z0, z1, z2) -> c2 NATS(z0) -> c7 ACTIVATE(z0) -> c12 NATS(z0) -> c6 SIEVE(z0) -> c5 ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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))))) ---------------------------------------- (30) 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 ---------------------------------------- (31) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: zprimes -> sieve(nats(s(s(0)))) ---------------------------------------- (32) 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 ---------------------------------------- (33) 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)) ---------------------------------------- (34) 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 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (36) 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 ---------------------------------------- (37) 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))))) ---------------------------------------- (38) 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 ---------------------------------------- (39) 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))))) ---------------------------------------- (40) 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 ---------------------------------------- (41) 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))) ---------------------------------------- (42) 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 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (45) 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))) ---------------------------------------- (46) 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 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (48) 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 ---------------------------------------- (49) 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)) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: SIEVE(cons(s(x0), n__nats(z0))) -> c4(FILTER(n__nats(z0), x0, x0)) ---------------------------------------- (52) 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 ---------------------------------------- (53) 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))) ---------------------------------------- (54) 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 ---------------------------------------- (55) 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))) ---------------------------------------- (56) 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 ---------------------------------------- (57) 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)) ---------------------------------------- (58) 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 ---------------------------------------- (59) 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))) ---------------------------------------- (60) 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 ---------------------------------------- (61) 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)) ---------------------------------------- (62) 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 ---------------------------------------- (63) 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)))) ---------------------------------------- (64) 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 ---------------------------------------- (65) 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))))) ---------------------------------------- (66) 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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing tuple parts ---------------------------------------- (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: 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 ---------------------------------------- (69) 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))) ---------------------------------------- (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: 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 ---------------------------------------- (71) 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))))) ---------------------------------------- (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: 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 ---------------------------------------- (73) 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))) ---------------------------------------- (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: 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 ---------------------------------------- (75) 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))))) ---------------------------------------- (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: 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 ---------------------------------------- (77) 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))) ---------------------------------------- (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: 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 ---------------------------------------- (79) 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))))) ---------------------------------------- (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: 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 ---------------------------------------- (81) 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))) ---------------------------------------- (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: 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 ---------------------------------------- (83) 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))))) ---------------------------------------- (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: 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 ---------------------------------------- (85) 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)) ---------------------------------------- (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: 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 ---------------------------------------- (87) 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)) ---------------------------------------- (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: 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 ---------------------------------------- (89) 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)) ---------------------------------------- (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(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 ---------------------------------------- (91) 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)) ---------------------------------------- (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(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 ---------------------------------------- (93) 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)))))) ---------------------------------------- (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: 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 ---------------------------------------- (95) 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)))) ---------------------------------------- (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: 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 ---------------------------------------- (97) 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)))))) ---------------------------------------- (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), 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 ---------------------------------------- (99) 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)))) ---------------------------------------- (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__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 ---------------------------------------- (101) 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)))))) ---------------------------------------- (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__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 ---------------------------------------- (103) 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)) ---------------------------------------- (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)))) 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 ---------------------------------------- (105) 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)) ---------------------------------------- (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)))) 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 ---------------------------------------- (107) 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))) ---------------------------------------- (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)))) 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 ---------------------------------------- (109) 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))) ---------------------------------------- (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)))) 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 ---------------------------------------- (111) 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))) ---------------------------------------- (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)))) 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 ---------------------------------------- (113) 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))) ---------------------------------------- (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)))) 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 ---------------------------------------- (115) 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))) ---------------------------------------- (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)))) 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 ---------------------------------------- (117) 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))) ---------------------------------------- (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__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 ---------------------------------------- (119) 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))))))) ---------------------------------------- (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__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 ---------------------------------------- (121) 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))))) ---------------------------------------- (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__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 ---------------------------------------- (123) 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))))))) ---------------------------------------- (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__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 ---------------------------------------- (125) 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))))) ---------------------------------------- (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), 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 ---------------------------------------- (127) 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))))))) ---------------------------------------- (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__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 ---------------------------------------- (129) 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))) ---------------------------------------- (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))))) 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 ---------------------------------------- (131) 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))) ---------------------------------------- (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))))) 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 ---------------------------------------- (133) 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))) ---------------------------------------- (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))))) 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 ---------------------------------------- (135) 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))) ---------------------------------------- (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(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 ---------------------------------------- (137) 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))))))) ---------------------------------------- (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(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 ---------------------------------------- (139) 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))))) ---------------------------------------- (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(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 ---------------------------------------- (141) 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))))))) ---------------------------------------- (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(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 ---------------------------------------- (143) 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))))) ---------------------------------------- (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__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