KILLED
proof of input_wOrdFzudyA.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxRelTRS
    (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 13 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 27.9 s]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 19.8 s]
    (18) BEST
        (19) proven lower bound
            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
            (21) BOUNDS(n^1, INF)
        (22) typed CpxTrs
(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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CpxRelTRS
        (33) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTRS
        (35) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (36) CpxWeightedTrs
            (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (38) CpxTypedWeightedTrs
            (39) CompletionProof [UPPER BOUND(ID), 0 ms]
            (40) CpxTypedWeightedCompleteTrs
                (41) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (42) CpxTypedWeightedCompleteTrs
                (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms]
                (44) CpxRNTS
                (45) InliningProof [UPPER BOUND(ID), 659 ms]
                (46) CpxRNTS
                (47) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (48) CpxRNTS
                (49) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
                (50) CpxRNTS
                (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (52) CpxRNTS
                (53) IntTrsBoundProof [UPPER BOUND(ID), 184 ms]
                (54) CpxRNTS
                (55) IntTrsBoundProof [UPPER BOUND(ID), 16 ms]
                (56) CpxRNTS
                (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (58) CpxRNTS
                (59) IntTrsBoundProof [UPPER BOUND(ID), 71 ms]
                (60) CpxRNTS
                (61) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
                (62) CpxRNTS
                (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (64) CpxRNTS
                (65) IntTrsBoundProof [UPPER BOUND(ID), 168 ms]
                (66) CpxRNTS
                (67) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
                (68) CpxRNTS
                (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
                (71) IntTrsBoundProof [UPPER BOUND(ID), 54 ms]
                (72) CpxRNTS
                (73) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
                (74) CpxRNTS
                (75) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (76) CpxRNTS
                (77) IntTrsBoundProof [UPPER BOUND(ID), 89 ms]
                (78) CpxRNTS
                (79) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
                (80) CpxRNTS
                (81) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (82) CpxRNTS
                (83) IntTrsBoundProof [UPPER BOUND(ID), 4265 ms]
                (84) CpxRNTS
                (85) IntTrsBoundProof [UPPER BOUND(ID), 304 ms]
                (86) CpxRNTS
                (87) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (88) CpxRNTS
                (89) IntTrsBoundProof [UPPER BOUND(ID), 2924 ms]
                (90) CpxRNTS
                (91) IntTrsBoundProof [UPPER BOUND(ID), 3300 ms]
                (92) CpxRNTS
            (93) CompletionProof [UPPER BOUND(ID), 0 ms]
            (94) CpxTypedWeightedCompleteTrs
                (95) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (96) CpxRNTS
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 43 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 77 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 9 ms]
        (154) CdtProblem
        (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (158) CdtProblem
        (159) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 111 ms]
        (160) CdtProblem
        (161) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 140 ms]
        (162) CdtProblem
        (163) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtRewritingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (166) CdtProblem
        (167) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (170) CdtProblem
        (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (174) CdtProblem
        (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms]
        (176) CdtProblem
        (177) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtRewritingProof [BOTH BOUNDS(ID, ID), 31 ms]
        (184) CdtProblem
        (185) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 23 ms]
        (186) CdtProblem
        (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 147 ms]
        (190) CdtProblem
        (191) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 151 ms]
        (192) CdtProblem
        (193) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (194) CdtProblem
        (195) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (196) CdtProblem
        (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
        (198) CdtProblem
        (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (200) CdtProblem
        (201) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (202) CdtProblem
        (203) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 5 ms]
        (204) CdtProblem
        (205) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (206) CdtProblem
        (207) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (208) CdtProblem
        (209) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (210) CdtProblem
        (211) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (212) CdtProblem
        (213) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (214) CdtProblem
        (215) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (216) CdtProblem
        (217) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 13 ms]
        (218) CdtProblem
        (219) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 18 ms]
        (220) CdtProblem
        (221) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (222) CdtProblem
        (223) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 11 ms]
        (224) CdtProblem
        (225) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (226) CdtProblem
(227) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(228) CpxWeightedTrs
    (229) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (230) CpxTypedWeightedTrs
    (231) CompletionProof [UPPER BOUND(ID), 0 ms]
    (232) CpxTypedWeightedCompleteTrs
        (233) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (234) CpxTypedWeightedCompleteTrs
        (235) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (236) CpxRNTS
        (237) InliningProof [UPPER BOUND(ID), 345 ms]
        (238) CpxRNTS
        (239) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (240) CpxRNTS
        (241) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (242) CpxRNTS
        (243) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (244) CpxRNTS
        (245) IntTrsBoundProof [UPPER BOUND(ID), 119 ms]
        (246) CpxRNTS
        (247) IntTrsBoundProof [UPPER BOUND(ID), 26 ms]
        (248) CpxRNTS
        (249) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (250) CpxRNTS
        (251) IntTrsBoundProof [UPPER BOUND(ID), 216 ms]
        (252) CpxRNTS
        (253) IntTrsBoundProof [UPPER BOUND(ID), 66 ms]
        (254) CpxRNTS
        (255) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (256) CpxRNTS
        (257) IntTrsBoundProof [UPPER BOUND(ID), 200 ms]
        (258) CpxRNTS
        (259) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
        (260) CpxRNTS
        (261) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (262) CpxRNTS
        (263) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
        (264) CpxRNTS
        (265) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
        (266) CpxRNTS
        (267) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (268) CpxRNTS
        (269) IntTrsBoundProof [UPPER BOUND(ID), 3208 ms]
        (270) CpxRNTS
        (271) IntTrsBoundProof [UPPER BOUND(ID), 272 ms]
        (272) CpxRNTS
        (273) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (274) CpxRNTS
        (275) IntTrsBoundProof [UPPER BOUND(ID), 3400 ms]
        (276) CpxRNTS
        (277) IntTrsBoundProof [UPPER BOUND(ID), 479 ms]
        (278) CpxRNTS
    (279) CompletionProof [UPPER BOUND(ID), 0 ms]
    (280) CpxTypedWeightedCompleteTrs
        (281) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms]
        (282) CpxRNTS


----------------------------------------

(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:

   from(X) -> cons(X, n__from(n__s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
   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:

   from(X) -> cons(X, n__from(n__s(X)))
   length(n__nil) -> 0'
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
   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:

   from(X) -> cons(X, n__from(n__s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
   activate(X) -> X

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(5) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12
S tuples:
   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, s_1, nil, cons_2, activate_1

Defined Pair Symbols:   FROM_1, LENGTH_1, LENGTH1_1, S_1, NIL, CONS_2, ACTIVATE_1

Compound Symbols:   c_1, c1, c2, c3_3, c4_2, c5, c6, c7, c8_2, c9_2, c10_1, c11_2, c12


----------------------------------------

(7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12

The (relative) TRS S consists of the following rules:

   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(9) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12

The (relative) TRS S consists of the following rules:

   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0'
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(11) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(12)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
FROM(z0) -> c1
LENGTH(n__nil) -> c2
LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S(z0) -> c5
NIL -> c6
CONS(z0, z1) -> c7
ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__nil) -> c10(NIL)
ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
ACTIVATE(z0) -> c12
from(z0) -> cons(z0, n__from(n__s(z0)))
from(z0) -> n__from(z0)
length(n__nil) -> 0'
length(n__cons(z0, z1)) -> s(length1(activate(z1)))
length1(z0) -> length(activate(z0))
s(z0) -> n__s(z0)
nil -> n__nil
cons(z0, z1) -> n__cons(z0, z1)
activate(n__from(z0)) -> from(activate(z0))
activate(n__s(z0)) -> s(activate(z0))
activate(n__nil) -> nil
activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
activate(z0) -> z0

Types:
FROM :: n__s:n__from:n__nil:n__cons:0' -> c:c1
c :: c7 -> c:c1
CONS :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> c7
n__from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
n__s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c1 :: c:c1
LENGTH :: n__s:n__from:n__nil:n__cons:0' -> c2:c3
n__nil :: n__s:n__from:n__nil:n__cons:0'
c2 :: c2:c3
n__cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c3 :: c5 -> c4 -> c8:c9:c10:c11:c12 -> c2:c3
S :: n__s:n__from:n__nil:n__cons:0' -> c5
length1 :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
activate :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
LENGTH1 :: n__s:n__from:n__nil:n__cons:0' -> c4
ACTIVATE :: n__s:n__from:n__nil:n__cons:0' -> c8:c9:c10:c11:c12
c4 :: c2:c3 -> c8:c9:c10:c11:c12 -> c4
c5 :: c5
NIL :: c6
c6 :: c6
c7 :: c7
c8 :: c:c1 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c9 :: c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c10 :: c6 -> c8:c9:c10:c11:c12
c11 :: c7 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c12 :: c8:c9:c10:c11:c12
from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
length :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
0' :: n__s:n__from:n__nil:n__cons:0'
s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
nil :: n__s:n__from:n__nil:n__cons:0'
hole_c:c11_13 :: c:c1
hole_n__s:n__from:n__nil:n__cons:0'2_13 :: n__s:n__from:n__nil:n__cons:0'
hole_c73_13 :: c7
hole_c2:c34_13 :: c2:c3
hole_c55_13 :: c5
hole_c46_13 :: c4
hole_c8:c9:c10:c11:c127_13 :: c8:c9:c10:c11:c12
hole_c68_13 :: c6
gen_n__s:n__from:n__nil:n__cons:0'9_13 :: Nat -> n__s:n__from:n__nil:n__cons:0'
gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12

----------------------------------------

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
LENGTH, length1, activate, LENGTH1, ACTIVATE, length

They will be analysed ascendingly in the following order:
length1 < LENGTH
activate < LENGTH
LENGTH = LENGTH1
ACTIVATE < LENGTH
activate < length1
length1 = length
activate < LENGTH1
activate < ACTIVATE
activate < length
ACTIVATE < LENGTH1

----------------------------------------

(14)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
FROM(z0) -> c1
LENGTH(n__nil) -> c2
LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S(z0) -> c5
NIL -> c6
CONS(z0, z1) -> c7
ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__nil) -> c10(NIL)
ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
ACTIVATE(z0) -> c12
from(z0) -> cons(z0, n__from(n__s(z0)))
from(z0) -> n__from(z0)
length(n__nil) -> 0'
length(n__cons(z0, z1)) -> s(length1(activate(z1)))
length1(z0) -> length(activate(z0))
s(z0) -> n__s(z0)
nil -> n__nil
cons(z0, z1) -> n__cons(z0, z1)
activate(n__from(z0)) -> from(activate(z0))
activate(n__s(z0)) -> s(activate(z0))
activate(n__nil) -> nil
activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
activate(z0) -> z0

Types:
FROM :: n__s:n__from:n__nil:n__cons:0' -> c:c1
c :: c7 -> c:c1
CONS :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> c7
n__from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
n__s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c1 :: c:c1
LENGTH :: n__s:n__from:n__nil:n__cons:0' -> c2:c3
n__nil :: n__s:n__from:n__nil:n__cons:0'
c2 :: c2:c3
n__cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c3 :: c5 -> c4 -> c8:c9:c10:c11:c12 -> c2:c3
S :: n__s:n__from:n__nil:n__cons:0' -> c5
length1 :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
activate :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
LENGTH1 :: n__s:n__from:n__nil:n__cons:0' -> c4
ACTIVATE :: n__s:n__from:n__nil:n__cons:0' -> c8:c9:c10:c11:c12
c4 :: c2:c3 -> c8:c9:c10:c11:c12 -> c4
c5 :: c5
NIL :: c6
c6 :: c6
c7 :: c7
c8 :: c:c1 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c9 :: c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c10 :: c6 -> c8:c9:c10:c11:c12
c11 :: c7 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c12 :: c8:c9:c10:c11:c12
from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
length :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
0' :: n__s:n__from:n__nil:n__cons:0'
s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
nil :: n__s:n__from:n__nil:n__cons:0'
hole_c:c11_13 :: c:c1
hole_n__s:n__from:n__nil:n__cons:0'2_13 :: n__s:n__from:n__nil:n__cons:0'
hole_c73_13 :: c7
hole_c2:c34_13 :: c2:c3
hole_c55_13 :: c5
hole_c46_13 :: c4
hole_c8:c9:c10:c11:c127_13 :: c8:c9:c10:c11:c12
hole_c68_13 :: c6
gen_n__s:n__from:n__nil:n__cons:0'9_13 :: Nat -> n__s:n__from:n__nil:n__cons:0'
gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12


Generator Equations:
gen_n__s:n__from:n__nil:n__cons:0'9_13(0) <=> n__nil
gen_n__s:n__from:n__nil:n__cons:0'9_13(+(x, 1)) <=> n__from(gen_n__s:n__from:n__nil:n__cons:0'9_13(x))
gen_c8:c9:c10:c11:c1210_13(0) <=> c10(c6)
gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c(c7), gen_c8:c9:c10:c11:c1210_13(x))


The following defined symbols remain to be analysed:
activate, LENGTH, length1, LENGTH1, ACTIVATE, length

They will be analysed ascendingly in the following order:
length1 < LENGTH
activate < LENGTH
LENGTH = LENGTH1
ACTIVATE < LENGTH
activate < length1
length1 = length
activate < LENGTH1
activate < ACTIVATE
activate < length
ACTIVATE < LENGTH1

----------------------------------------

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, n12_13))) -> *11_13, rt in Omega(0)

Induction Base:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, 0)))

Induction Step:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, +(n12_13, 1)))) ->_R^Omega(0)
from(activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, n12_13)))) ->_IH
from(*11_13)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(16)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
FROM(z0) -> c1
LENGTH(n__nil) -> c2
LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S(z0) -> c5
NIL -> c6
CONS(z0, z1) -> c7
ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__nil) -> c10(NIL)
ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
ACTIVATE(z0) -> c12
from(z0) -> cons(z0, n__from(n__s(z0)))
from(z0) -> n__from(z0)
length(n__nil) -> 0'
length(n__cons(z0, z1)) -> s(length1(activate(z1)))
length1(z0) -> length(activate(z0))
s(z0) -> n__s(z0)
nil -> n__nil
cons(z0, z1) -> n__cons(z0, z1)
activate(n__from(z0)) -> from(activate(z0))
activate(n__s(z0)) -> s(activate(z0))
activate(n__nil) -> nil
activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
activate(z0) -> z0

Types:
FROM :: n__s:n__from:n__nil:n__cons:0' -> c:c1
c :: c7 -> c:c1
CONS :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> c7
n__from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
n__s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c1 :: c:c1
LENGTH :: n__s:n__from:n__nil:n__cons:0' -> c2:c3
n__nil :: n__s:n__from:n__nil:n__cons:0'
c2 :: c2:c3
n__cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c3 :: c5 -> c4 -> c8:c9:c10:c11:c12 -> c2:c3
S :: n__s:n__from:n__nil:n__cons:0' -> c5
length1 :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
activate :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
LENGTH1 :: n__s:n__from:n__nil:n__cons:0' -> c4
ACTIVATE :: n__s:n__from:n__nil:n__cons:0' -> c8:c9:c10:c11:c12
c4 :: c2:c3 -> c8:c9:c10:c11:c12 -> c4
c5 :: c5
NIL :: c6
c6 :: c6
c7 :: c7
c8 :: c:c1 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c9 :: c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c10 :: c6 -> c8:c9:c10:c11:c12
c11 :: c7 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c12 :: c8:c9:c10:c11:c12
from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
length :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
0' :: n__s:n__from:n__nil:n__cons:0'
s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
nil :: n__s:n__from:n__nil:n__cons:0'
hole_c:c11_13 :: c:c1
hole_n__s:n__from:n__nil:n__cons:0'2_13 :: n__s:n__from:n__nil:n__cons:0'
hole_c73_13 :: c7
hole_c2:c34_13 :: c2:c3
hole_c55_13 :: c5
hole_c46_13 :: c4
hole_c8:c9:c10:c11:c127_13 :: c8:c9:c10:c11:c12
hole_c68_13 :: c6
gen_n__s:n__from:n__nil:n__cons:0'9_13 :: Nat -> n__s:n__from:n__nil:n__cons:0'
gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12


Lemmas:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, n12_13))) -> *11_13, rt in Omega(0)


Generator Equations:
gen_n__s:n__from:n__nil:n__cons:0'9_13(0) <=> n__nil
gen_n__s:n__from:n__nil:n__cons:0'9_13(+(x, 1)) <=> n__from(gen_n__s:n__from:n__nil:n__cons:0'9_13(x))
gen_c8:c9:c10:c11:c1210_13(0) <=> c10(c6)
gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c(c7), gen_c8:c9:c10:c11:c1210_13(x))


The following defined symbols remain to be analysed:
ACTIVATE, LENGTH, length1, LENGTH1, length

They will be analysed ascendingly in the following order:
length1 < LENGTH
LENGTH = LENGTH1
ACTIVATE < LENGTH
length1 = length
ACTIVATE < LENGTH1

----------------------------------------

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13)) -> gen_c8:c9:c10:c11:c1210_13(n398903_13), rt in Omega(1 + n398903_13)

Induction Base:
ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(0)) ->_R^Omega(1)
c10(NIL) ->_R^Omega(1)
c10(c6)

Induction Step:
ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(n398903_13, 1))) ->_R^Omega(1)
c8(FROM(activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))), ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))) ->_R^Omega(0)
c8(FROM(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13)), ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))) ->_R^Omega(1)
c8(c(CONS(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13), n__from(n__s(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))))), ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))) ->_R^Omega(1)
c8(c(c7), ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13))) ->_IH
c8(c(c7), gen_c8:c9:c10:c11:c1210_13(c398904_13))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(18)
Complex Obligation (BEST)

----------------------------------------

(19)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
FROM(z0) -> c1
LENGTH(n__nil) -> c2
LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S(z0) -> c5
NIL -> c6
CONS(z0, z1) -> c7
ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__nil) -> c10(NIL)
ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
ACTIVATE(z0) -> c12
from(z0) -> cons(z0, n__from(n__s(z0)))
from(z0) -> n__from(z0)
length(n__nil) -> 0'
length(n__cons(z0, z1)) -> s(length1(activate(z1)))
length1(z0) -> length(activate(z0))
s(z0) -> n__s(z0)
nil -> n__nil
cons(z0, z1) -> n__cons(z0, z1)
activate(n__from(z0)) -> from(activate(z0))
activate(n__s(z0)) -> s(activate(z0))
activate(n__nil) -> nil
activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
activate(z0) -> z0

Types:
FROM :: n__s:n__from:n__nil:n__cons:0' -> c:c1
c :: c7 -> c:c1
CONS :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> c7
n__from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
n__s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c1 :: c:c1
LENGTH :: n__s:n__from:n__nil:n__cons:0' -> c2:c3
n__nil :: n__s:n__from:n__nil:n__cons:0'
c2 :: c2:c3
n__cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c3 :: c5 -> c4 -> c8:c9:c10:c11:c12 -> c2:c3
S :: n__s:n__from:n__nil:n__cons:0' -> c5
length1 :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
activate :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
LENGTH1 :: n__s:n__from:n__nil:n__cons:0' -> c4
ACTIVATE :: n__s:n__from:n__nil:n__cons:0' -> c8:c9:c10:c11:c12
c4 :: c2:c3 -> c8:c9:c10:c11:c12 -> c4
c5 :: c5
NIL :: c6
c6 :: c6
c7 :: c7
c8 :: c:c1 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c9 :: c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c10 :: c6 -> c8:c9:c10:c11:c12
c11 :: c7 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c12 :: c8:c9:c10:c11:c12
from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
length :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
0' :: n__s:n__from:n__nil:n__cons:0'
s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
nil :: n__s:n__from:n__nil:n__cons:0'
hole_c:c11_13 :: c:c1
hole_n__s:n__from:n__nil:n__cons:0'2_13 :: n__s:n__from:n__nil:n__cons:0'
hole_c73_13 :: c7
hole_c2:c34_13 :: c2:c3
hole_c55_13 :: c5
hole_c46_13 :: c4
hole_c8:c9:c10:c11:c127_13 :: c8:c9:c10:c11:c12
hole_c68_13 :: c6
gen_n__s:n__from:n__nil:n__cons:0'9_13 :: Nat -> n__s:n__from:n__nil:n__cons:0'
gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12


Lemmas:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, n12_13))) -> *11_13, rt in Omega(0)


Generator Equations:
gen_n__s:n__from:n__nil:n__cons:0'9_13(0) <=> n__nil
gen_n__s:n__from:n__nil:n__cons:0'9_13(+(x, 1)) <=> n__from(gen_n__s:n__from:n__nil:n__cons:0'9_13(x))
gen_c8:c9:c10:c11:c1210_13(0) <=> c10(c6)
gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c(c7), gen_c8:c9:c10:c11:c1210_13(x))


The following defined symbols remain to be analysed:
ACTIVATE, LENGTH, length1, LENGTH1, length

They will be analysed ascendingly in the following order:
length1 < LENGTH
LENGTH = LENGTH1
ACTIVATE < LENGTH
length1 = length
ACTIVATE < LENGTH1

----------------------------------------

(20) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(21)
BOUNDS(n^1, INF)

----------------------------------------

(22)
Obligation:
Innermost TRS:
Rules:
FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
FROM(z0) -> c1
LENGTH(n__nil) -> c2
LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S(z0) -> c5
NIL -> c6
CONS(z0, z1) -> c7
ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
ACTIVATE(n__nil) -> c10(NIL)
ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
ACTIVATE(z0) -> c12
from(z0) -> cons(z0, n__from(n__s(z0)))
from(z0) -> n__from(z0)
length(n__nil) -> 0'
length(n__cons(z0, z1)) -> s(length1(activate(z1)))
length1(z0) -> length(activate(z0))
s(z0) -> n__s(z0)
nil -> n__nil
cons(z0, z1) -> n__cons(z0, z1)
activate(n__from(z0)) -> from(activate(z0))
activate(n__s(z0)) -> s(activate(z0))
activate(n__nil) -> nil
activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
activate(z0) -> z0

Types:
FROM :: n__s:n__from:n__nil:n__cons:0' -> c:c1
c :: c7 -> c:c1
CONS :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> c7
n__from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
n__s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c1 :: c:c1
LENGTH :: n__s:n__from:n__nil:n__cons:0' -> c2:c3
n__nil :: n__s:n__from:n__nil:n__cons:0'
c2 :: c2:c3
n__cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
c3 :: c5 -> c4 -> c8:c9:c10:c11:c12 -> c2:c3
S :: n__s:n__from:n__nil:n__cons:0' -> c5
length1 :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
activate :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
LENGTH1 :: n__s:n__from:n__nil:n__cons:0' -> c4
ACTIVATE :: n__s:n__from:n__nil:n__cons:0' -> c8:c9:c10:c11:c12
c4 :: c2:c3 -> c8:c9:c10:c11:c12 -> c4
c5 :: c5
NIL :: c6
c6 :: c6
c7 :: c7
c8 :: c:c1 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c9 :: c5 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c10 :: c6 -> c8:c9:c10:c11:c12
c11 :: c7 -> c8:c9:c10:c11:c12 -> c8:c9:c10:c11:c12
c12 :: c8:c9:c10:c11:c12
from :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
cons :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
length :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
0' :: n__s:n__from:n__nil:n__cons:0'
s :: n__s:n__from:n__nil:n__cons:0' -> n__s:n__from:n__nil:n__cons:0'
nil :: n__s:n__from:n__nil:n__cons:0'
hole_c:c11_13 :: c:c1
hole_n__s:n__from:n__nil:n__cons:0'2_13 :: n__s:n__from:n__nil:n__cons:0'
hole_c73_13 :: c7
hole_c2:c34_13 :: c2:c3
hole_c55_13 :: c5
hole_c46_13 :: c4
hole_c8:c9:c10:c11:c127_13 :: c8:c9:c10:c11:c12
hole_c68_13 :: c6
gen_n__s:n__from:n__nil:n__cons:0'9_13 :: Nat -> n__s:n__from:n__nil:n__cons:0'
gen_c8:c9:c10:c11:c1210_13 :: Nat -> c8:c9:c10:c11:c12


Lemmas:
activate(gen_n__s:n__from:n__nil:n__cons:0'9_13(+(1, n12_13))) -> *11_13, rt in Omega(0)
ACTIVATE(gen_n__s:n__from:n__nil:n__cons:0'9_13(n398903_13)) -> gen_c8:c9:c10:c11:c1210_13(n398903_13), rt in Omega(1 + n398903_13)


Generator Equations:
gen_n__s:n__from:n__nil:n__cons:0'9_13(0) <=> n__nil
gen_n__s:n__from:n__nil:n__cons:0'9_13(+(x, 1)) <=> n__from(gen_n__s:n__from:n__nil:n__cons:0'9_13(x))
gen_c8:c9:c10:c11:c1210_13(0) <=> c10(c6)
gen_c8:c9:c10:c11:c1210_13(+(x, 1)) <=> c8(c(c7), gen_c8:c9:c10:c11:c1210_13(x))


The following defined symbols remain to be analysed:
length, LENGTH, length1, LENGTH1

They will be analysed ascendingly in the following order:
length1 < LENGTH
LENGTH = LENGTH1
length1 = length

----------------------------------------

(23) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12
S tuples:
   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   S(z0) -> c5
   NIL -> c6
   CONS(z0, z1) -> c7
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__nil) -> c10(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
   ACTIVATE(z0) -> c12
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, s_1, nil, cons_2, activate_1

Defined Pair Symbols:   FROM_1, LENGTH_1, LENGTH1_1, S_1, NIL, CONS_2, ACTIVATE_1

Compound Symbols:   c_1, c1, c2, c3_3, c4_2, c5, c6, c7, c8_2, c9_2, c10_1, c11_2, c12


----------------------------------------

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing nodes:
   ACTIVATE(n__nil) -> c10(NIL)
   LENGTH(n__nil) -> c2
   CONS(z0, z1) -> c7
   ACTIVATE(z0) -> c12
   NIL -> c6
   FROM(z0) -> c(CONS(z0, n__from(n__s(z0))))
   FROM(z0) -> c1
   S(z0) -> c5

----------------------------------------

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, s_1, nil, cons_2, activate_1

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_3, c4_2, c8_2, c9_2, c11_2


----------------------------------------

(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
Tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, s_1, nil, cons_2, activate_1

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c9_1, c11_1


----------------------------------------

(29) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))

----------------------------------------

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c9_1, c11_1


----------------------------------------

(31) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(32)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))

The (relative) TRS S consists of the following rules:

   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)

Rewrite Strategy: INNERMOST
----------------------------------------

(33) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(34)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(35) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(36)
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:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) [1]
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) [1]
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) [1]
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) [1]
   activate(n__from(z0)) -> from(activate(z0)) [0]
   activate(n__s(z0)) -> s(activate(z0)) [0]
   activate(n__nil) -> nil [0]
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(n__s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   s(z0) -> n__s(z0) [0]
   nil -> n__nil [0]
   cons(z0, z1) -> n__cons(z0, z1) [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(37) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(38)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) [1]
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) [1]
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) [1]
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) [1]
   activate(n__from(z0)) -> from(activate(z0)) [0]
   activate(n__s(z0)) -> s(activate(z0)) [0]
   activate(n__nil) -> nil [0]
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(n__s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   s(z0) -> n__s(z0) [0]
   nil -> n__nil [0]
   cons(z0, z1) -> n__cons(z0, z1) [0]

The TRS has the following type information:
LENGTH1 :: n__cons:n__from:n__s:n__nil -> c4
c4 :: c3 -> c8:c9:c11 -> c4
LENGTH :: n__cons:n__from:n__s:n__nil -> c3
activate :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
ACTIVATE :: n__cons:n__from:n__s:n__nil -> c8:c9:c11
n__cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c3 :: c4 -> c8:c9:c11 -> c3
n__from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c8 :: c8:c9:c11 -> c8:c9:c11
n__s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c9 :: c8:c9:c11 -> c8:c9:c11
c11 :: c8:c9:c11 -> c8:c9:c11
from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
n__nil :: n__cons:n__from:n__s:n__nil
nil :: n__cons:n__from:n__s:n__nil
cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil

Rewrite Strategy: INNERMOST
----------------------------------------

(39) 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:

   LENGTH1_1
   LENGTH_1
   ACTIVATE_1

(c) The following functions are completely defined:

   activate_1
   from_1
   s_1
   nil
   cons_2

Due to the following rules being added:

   activate(v0) -> n__nil [0]
   from(v0) -> n__nil [0]
   s(v0) -> n__nil [0]
   nil -> n__nil [0]
   cons(v0, v1) -> n__nil [0]

And the following fresh constants:    const, const1, const2

----------------------------------------

(40)
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:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) [1]
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) [1]
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) [1]
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) [1]
   activate(n__from(z0)) -> from(activate(z0)) [0]
   activate(n__s(z0)) -> s(activate(z0)) [0]
   activate(n__nil) -> nil [0]
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(n__s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   s(z0) -> n__s(z0) [0]
   nil -> n__nil [0]
   cons(z0, z1) -> n__cons(z0, z1) [0]
   activate(v0) -> n__nil [0]
   from(v0) -> n__nil [0]
   s(v0) -> n__nil [0]
   nil -> n__nil [0]
   cons(v0, v1) -> n__nil [0]

The TRS has the following type information:
LENGTH1 :: n__cons:n__from:n__s:n__nil -> c4
c4 :: c3 -> c8:c9:c11 -> c4
LENGTH :: n__cons:n__from:n__s:n__nil -> c3
activate :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
ACTIVATE :: n__cons:n__from:n__s:n__nil -> c8:c9:c11
n__cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c3 :: c4 -> c8:c9:c11 -> c3
n__from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c8 :: c8:c9:c11 -> c8:c9:c11
n__s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c9 :: c8:c9:c11 -> c8:c9:c11
c11 :: c8:c9:c11 -> c8:c9:c11
from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
n__nil :: n__cons:n__from:n__s:n__nil
nil :: n__cons:n__from:n__s:n__nil
cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
const :: c4
const1 :: c3
const2 :: c8:c9:c11

Rewrite Strategy: INNERMOST
----------------------------------------

(41) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(42)
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:

   LENGTH1(n__from(z0')) -> c4(LENGTH(from(activate(z0'))), ACTIVATE(n__from(z0'))) [1]
   LENGTH1(n__s(z0'')) -> c4(LENGTH(s(activate(z0''))), ACTIVATE(n__s(z0''))) [1]
   LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil)) [1]
   LENGTH1(n__cons(z01, z1')) -> c4(LENGTH(cons(activate(z01), z1')), ACTIVATE(n__cons(z01, z1'))) [1]
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) [1]
   LENGTH1(z0) -> c4(LENGTH(n__nil), ACTIVATE(z0)) [1]
   LENGTH(n__cons(z0, n__from(z02))) -> c3(LENGTH1(from(activate(z02))), ACTIVATE(n__from(z02))) [1]
   LENGTH(n__cons(z0, n__s(z03))) -> c3(LENGTH1(s(activate(z03))), ACTIVATE(n__s(z03))) [1]
   LENGTH(n__cons(z0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil)) [1]
   LENGTH(n__cons(z0, n__cons(z04, z1''))) -> c3(LENGTH1(cons(activate(z04), z1'')), ACTIVATE(n__cons(z04, z1''))) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(z1), ACTIVATE(z1)) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(n__nil), ACTIVATE(z1)) [1]
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) [1]
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) [1]
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) [1]
   activate(n__from(n__from(z05))) -> from(from(activate(z05))) [0]
   activate(n__from(n__s(z06))) -> from(s(activate(z06))) [0]
   activate(n__from(n__nil)) -> from(nil) [0]
   activate(n__from(n__cons(z07, z11))) -> from(cons(activate(z07), z11)) [0]
   activate(n__from(z0)) -> from(z0) [0]
   activate(n__from(z0)) -> from(n__nil) [0]
   activate(n__s(n__from(z08))) -> s(from(activate(z08))) [0]
   activate(n__s(n__s(z09))) -> s(s(activate(z09))) [0]
   activate(n__s(n__nil)) -> s(nil) [0]
   activate(n__s(n__cons(z010, z12))) -> s(cons(activate(z010), z12)) [0]
   activate(n__s(z0)) -> s(z0) [0]
   activate(n__s(z0)) -> s(n__nil) [0]
   activate(n__nil) -> nil [0]
   activate(n__cons(n__from(z011), z1)) -> cons(from(activate(z011)), z1) [0]
   activate(n__cons(n__s(z012), z1)) -> cons(s(activate(z012)), z1) [0]
   activate(n__cons(n__nil, z1)) -> cons(nil, z1) [0]
   activate(n__cons(n__cons(z013, z13), z1)) -> cons(cons(activate(z013), z13), z1) [0]
   activate(n__cons(z0, z1)) -> cons(z0, z1) [0]
   activate(n__cons(z0, z1)) -> cons(n__nil, z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(n__s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   s(z0) -> n__s(z0) [0]
   nil -> n__nil [0]
   cons(z0, z1) -> n__cons(z0, z1) [0]
   activate(v0) -> n__nil [0]
   from(v0) -> n__nil [0]
   s(v0) -> n__nil [0]
   nil -> n__nil [0]
   cons(v0, v1) -> n__nil [0]

The TRS has the following type information:
LENGTH1 :: n__cons:n__from:n__s:n__nil -> c4
c4 :: c3 -> c8:c9:c11 -> c4
LENGTH :: n__cons:n__from:n__s:n__nil -> c3
activate :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
ACTIVATE :: n__cons:n__from:n__s:n__nil -> c8:c9:c11
n__cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c3 :: c4 -> c8:c9:c11 -> c3
n__from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c8 :: c8:c9:c11 -> c8:c9:c11
n__s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
c9 :: c8:c9:c11 -> c8:c9:c11
c11 :: c8:c9:c11 -> c8:c9:c11
from :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
s :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
n__nil :: n__cons:n__from:n__s:n__nil
nil :: n__cons:n__from:n__s:n__nil
cons :: n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil -> n__cons:n__from:n__s:n__nil
const :: c4
const1 :: c3
const2 :: c8:c9:c11

Rewrite Strategy: INNERMOST
----------------------------------------

(43) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   n__nil => 0
   const => 0
   const1 => 0
   const2 => 0

----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(nil) + ACTIVATE(0) :|: z0 >= 0, z = 1 + z0 + 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z0) + ACTIVATE(z0) :|: z = z0, z0 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z0''))) + ACTIVATE(1 + z0'') :|: z0'' >= 0, z = 1 + z0''
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(nil) + ACTIVATE(0) :|: z = 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z0'))) + ACTIVATE(1 + z0') :|: z0' >= 0, z = 1 + z0'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z0) :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> s(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> s(s(activate(z09))) :|: z = 1 + (1 + z09), z09 >= 0
   activate(z) -{ 0 }-> s(nil) :|: z = 1 + 0
   activate(z) -{ 0 }-> s(from(activate(z08))) :|: z08 >= 0, z = 1 + (1 + z08)
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> nil :|: z = 0
   activate(z) -{ 0 }-> from(z0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> from(s(activate(z06))) :|: z06 >= 0, z = 1 + (1 + z06)
   activate(z) -{ 0 }-> from(nil) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(from(activate(z05))) :|: z05 >= 0, z = 1 + (1 + z05)
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> from(0) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(nil, z1) :|: z1 >= 0, z = 1 + 0 + z1
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> cons(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cons(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   from(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0


----------------------------------------

(45) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   nil -{ 0 }-> 0 :|: 
   cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cons(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = z0, z0 >= 0

----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z0 >= 0, z = 1 + z0 + 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z0) + ACTIVATE(z0) :|: z = z0, z0 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z0''))) + ACTIVATE(1 + z0'') :|: z0'' >= 0, z = 1 + z0''
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z0'))) + ACTIVATE(1 + z0') :|: z0' >= 0, z = 1 + z0'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z0) :|: z = z0, z0 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> s(s(activate(z09))) :|: z = 1 + (1 + z09), z09 >= 0
   activate(z) -{ 0 }-> s(from(activate(z08))) :|: z08 >= 0, z = 1 + (1 + z08)
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z06))) :|: z06 >= 0, z = 1 + (1 + z06)
   activate(z) -{ 0 }-> from(from(activate(z05))) :|: z05 >= 0, z = 1 + (1 + z05)
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, z0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z = 1 + 0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z1 >= 0, z = 1 + 0 + z1, 0 = z0, z1' >= 0, z1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cons(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 0 :|: z = z0, z0 >= 0, v0 >= 0, v1 >= 0, z0 = v0, 1 + (1 + z0) = v1
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 1 + z0' + z1 :|: z = z0, z0 >= 0, z0 = z0', z1 >= 0, 1 + (1 + z0) = z1, z0' >= 0
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0


----------------------------------------

(47) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0


----------------------------------------

(49) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { from }
   { cons }
   { s }
   { nil }
   { ACTIVATE }
   { activate }
   { LENGTH, LENGTH1 }

----------------------------------------

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}

----------------------------------------

(51) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}

----------------------------------------

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

----------------------------------------

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: ?, size: O(n^1) [3 + 2*z]

----------------------------------------

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]

----------------------------------------

(57) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]

----------------------------------------

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: ?, size: O(n^1) [1 + z + z']

----------------------------------------

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(z0', 1 + (1 + z0')) :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']

----------------------------------------

(63) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']

----------------------------------------

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: s
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: s
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s(0) :|: z = 1 + 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]

----------------------------------------

(69) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(70)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]

----------------------------------------

(71) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(72)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: ?, size: O(1) [0]

----------------------------------------

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(74)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]

----------------------------------------

(75) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]

----------------------------------------

(77) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: ACTIVATE
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {ACTIVATE}, {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: ?, size: O(1) [0]

----------------------------------------

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: ACTIVATE
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(80)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z - 1) :|: z - 1 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(z1) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(s(activate(z03))) + ACTIVATE(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(from(activate(z02))) + ACTIVATE(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(cons(activate(z04), z1'')) + ACTIVATE(1 + z04 + z1'') :|: z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + ACTIVATE(0) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(z) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(s(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(from(activate(z - 1))) + ACTIVATE(1 + (z - 1)) :|: z - 1 >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(cons(activate(z01), z1')) + ACTIVATE(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(z) :|: z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + ACTIVATE(0) :|: z = 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]

----------------------------------------

(81) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s(activate(z03))) + s9 :|: s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(from(activate(z02))) + s15 :|: s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(cons(activate(z04), z1'')) + s13 :|: s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s(activate(z - 1))) + s8 :|: s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(from(activate(z - 1))) + s14 :|: s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(cons(activate(z01), z1')) + s12 :|: s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]

----------------------------------------

(83) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

----------------------------------------

(84)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s(activate(z03))) + s9 :|: s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(from(activate(z02))) + s15 :|: s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(cons(activate(z04), z1'')) + s13 :|: s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s(activate(z - 1))) + s8 :|: s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(from(activate(z - 1))) + s14 :|: s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(cons(activate(z01), z1')) + s12 :|: s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]
  activate: runtime: ?, size: EXP

----------------------------------------

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(86)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s(activate(z03))) + s9 :|: s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(from(activate(z02))) + s15 :|: s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(cons(activate(z04), z1'')) + s13 :|: s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s(activate(z - 1))) + s8 :|: s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(from(activate(z - 1))) + s14 :|: s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(cons(activate(z01), z1')) + s12 :|: s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> s(cons(activate(z010), z12)) :|: z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 0 }-> from(cons(activate(z07), z11)) :|: z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> cons(s(activate(z012)), z1) :|: z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> cons(from(activate(z011)), z1) :|: z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> cons(cons(activate(z013), z13), z1) :|: z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]
  activate: runtime: O(1) [0], size: EXP

----------------------------------------

(87) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(88)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s19) + s9 :|: s18 >= 0, s18 <= inf', s19 >= 0, s19 <= s18 + 1, s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(s26) + s13 :|: s25 >= 0, s25 <= inf2, s26 >= 0, s26 <= s25 + z1'' + 1, s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(s39) + s15 :|: s38 >= 0, s38 <= inf7, s39 >= 0, s39 <= 2 * s38 + 3, s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s17) + s8 :|: s16 >= 0, s16 <= inf, s17 >= 0, s17 <= s16 + 1, s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(s24) + s12 :|: s23 >= 0, s23 <= inf1, s24 >= 0, s24 <= s23 + z1' + 1, s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s37) + s14 :|: s36 >= 0, s36 <= inf6, s37 >= 0, s37 <= 2 * s36 + 3, s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> s22 :|: s20 >= 0, s20 <= inf'', s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s29 :|: s27 >= 0, s27 <= inf3, s28 >= 0, s28 <= s27 + z13 + 1, s29 >= 0, s29 <= s28 + z1 + 1, z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> s32 :|: s30 >= 0, s30 <= inf4, s31 >= 0, s31 <= s30 + z12 + 1, s32 >= 0, s32 <= s31 + 1, z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s35 :|: s33 >= 0, s33 <= inf5, s34 >= 0, s34 <= s33 + 1, s35 >= 0, s35 <= s34 + z1 + 1, z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> s42 :|: s40 >= 0, s40 <= inf8, s41 >= 0, s41 <= 2 * s40 + 3, s42 >= 0, s42 <= 2 * s41 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s45 :|: s43 >= 0, s43 <= inf9, s44 >= 0, s44 <= s43 + 1, s45 >= 0, s45 <= 2 * s44 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s48 :|: s46 >= 0, s46 <= inf10, s47 >= 0, s47 <= 2 * s46 + 3, s48 >= 0, s48 <= s47 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s51 :|: s49 >= 0, s49 <= inf11, s50 >= 0, s50 <= s49 + z11 + 1, s51 >= 0, s51 <= 2 * s50 + 3, z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> s54 :|: s52 >= 0, s52 <= inf12, s53 >= 0, s53 <= 2 * s52 + 3, s54 >= 0, s54 <= s53 + z1 + 1, z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]
  activate: runtime: O(1) [0], size: EXP

----------------------------------------

(89) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: LENGTH
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: LENGTH1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(90)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s19) + s9 :|: s18 >= 0, s18 <= inf', s19 >= 0, s19 <= s18 + 1, s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(s26) + s13 :|: s25 >= 0, s25 <= inf2, s26 >= 0, s26 <= s25 + z1'' + 1, s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(s39) + s15 :|: s38 >= 0, s38 <= inf7, s39 >= 0, s39 <= 2 * s38 + 3, s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s17) + s8 :|: s16 >= 0, s16 <= inf, s17 >= 0, s17 <= s16 + 1, s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(s24) + s12 :|: s23 >= 0, s23 <= inf1, s24 >= 0, s24 <= s23 + z1' + 1, s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s37) + s14 :|: s36 >= 0, s36 <= inf6, s37 >= 0, s37 <= 2 * s36 + 3, s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> s22 :|: s20 >= 0, s20 <= inf'', s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s29 :|: s27 >= 0, s27 <= inf3, s28 >= 0, s28 <= s27 + z13 + 1, s29 >= 0, s29 <= s28 + z1 + 1, z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> s32 :|: s30 >= 0, s30 <= inf4, s31 >= 0, s31 <= s30 + z12 + 1, s32 >= 0, s32 <= s31 + 1, z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s35 :|: s33 >= 0, s33 <= inf5, s34 >= 0, s34 <= s33 + 1, s35 >= 0, s35 <= s34 + z1 + 1, z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> s42 :|: s40 >= 0, s40 <= inf8, s41 >= 0, s41 <= 2 * s40 + 3, s42 >= 0, s42 <= 2 * s41 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s45 :|: s43 >= 0, s43 <= inf9, s44 >= 0, s44 <= s43 + 1, s45 >= 0, s45 <= 2 * s44 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s48 :|: s46 >= 0, s46 <= inf10, s47 >= 0, s47 <= 2 * s46 + 3, s48 >= 0, s48 <= s47 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s51 :|: s49 >= 0, s49 <= inf11, s50 >= 0, s50 <= s49 + z11 + 1, s51 >= 0, s51 <= 2 * s50 + 3, z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> s54 :|: s52 >= 0, s52 <= inf12, s53 >= 0, s53 <= 2 * s52 + 3, s54 >= 0, s54 <= s53 + z1 + 1, z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]
  activate: runtime: O(1) [0], size: EXP
  LENGTH: runtime: ?, size: O(1) [0]
  LENGTH1: runtime: ?, size: O(1) [1]

----------------------------------------

(91) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: LENGTH
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

----------------------------------------

(92)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ z }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z - 1 >= 0
   ACTIVATE(z) -{ 1 + z0 }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 2 + z03 }-> 1 + LENGTH1(s19) + s9 :|: s18 >= 0, s18 <= inf', s19 >= 0, s19 <= s18 + 1, s9 >= 0, s9 <= 0, z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0
   LENGTH(z) -{ 2 + z04 + z1'' }-> 1 + LENGTH1(s26) + s13 :|: s25 >= 0, s25 <= inf2, s26 >= 0, s26 <= s25 + z1'' + 1, s13 >= 0, s13 <= 0, z04 >= 0, z = 1 + z0 + (1 + z04 + z1''), z0 >= 0, z1'' >= 0
   LENGTH(z) -{ 2 + z02 }-> 1 + LENGTH1(s39) + s15 :|: s38 >= 0, s38 <= inf7, s39 >= 0, s39 <= 2 * s38 + 3, s15 >= 0, s15 <= 0, z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(z1) + s4 :|: s4 >= 0, s4 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(0) + s11 :|: s11 >= 0, s11 <= 0, z - 1 >= 0
   LENGTH(z) -{ 1 + z1 }-> 1 + LENGTH1(0) + s5 :|: s5 >= 0, s5 <= 0, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s17) + s8 :|: s16 >= 0, s16 <= inf, s17 >= 0, s17 <= s16 + 1, s8 >= 0, s8 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 2 + z01 + z1' }-> 1 + LENGTH(s24) + s12 :|: s23 >= 0, s23 <= inf1, s24 >= 0, s24 <= s23 + z1' + 1, s12 >= 0, s12 <= 0, z01 >= 0, z1' >= 0, z = 1 + z01 + z1'
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(s37) + s14 :|: s36 >= 0, s36 <= inf6, s37 >= 0, s37 <= 2 * s36 + 3, s14 >= 0, s14 <= 0, z - 1 >= 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(z) + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(0) + s10 :|: s10 >= 0, s10 <= 0, z = 0
   LENGTH1(z) -{ 1 + z }-> 1 + LENGTH(0) + s3 :|: s3 >= 0, s3 <= 0, z >= 0
   activate(z) -{ 0 }-> s :|: s >= 0, s <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> s' :|: s' >= 0, s' <= z0' + (1 + (1 + z0')) + 1, z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> s'' :|: s'' >= 0, s'' <= z0 + (1 + (1 + z0)) + 1, z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> s1 :|: s1 >= 0, s1 <= 0 + 1, z = 1 + 0
   activate(z) -{ 0 }-> s22 :|: s20 >= 0, s20 <= inf'', s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s29 :|: s27 >= 0, s27 <= inf3, s28 >= 0, s28 <= s27 + z13 + 1, s29 >= 0, s29 <= s28 + z1 + 1, z1 >= 0, z = 1 + (1 + z013 + z13) + z1, z013 >= 0, z13 >= 0
   activate(z) -{ 0 }-> s32 :|: s30 >= 0, s30 <= inf4, s31 >= 0, s31 <= s30 + z12 + 1, s32 >= 0, s32 <= s31 + 1, z12 >= 0, z = 1 + (1 + z010 + z12), z010 >= 0
   activate(z) -{ 0 }-> s35 :|: s33 >= 0, s33 <= inf5, s34 >= 0, s34 <= s33 + 1, s35 >= 0, s35 <= s34 + z1 + 1, z1 >= 0, z = 1 + (1 + z012) + z1, z012 >= 0
   activate(z) -{ 0 }-> s42 :|: s40 >= 0, s40 <= inf8, s41 >= 0, s41 <= 2 * s40 + 3, s42 >= 0, s42 <= 2 * s41 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s45 :|: s43 >= 0, s43 <= inf9, s44 >= 0, s44 <= s43 + 1, s45 >= 0, s45 <= 2 * s44 + 3, z - 2 >= 0
   activate(z) -{ 0 }-> s48 :|: s46 >= 0, s46 <= inf10, s47 >= 0, s47 <= 2 * s46 + 3, s48 >= 0, s48 <= s47 + 1, z - 2 >= 0
   activate(z) -{ 0 }-> s51 :|: s49 >= 0, s49 <= inf11, s50 >= 0, s50 <= s49 + z11 + 1, s51 >= 0, s51 <= 2 * s50 + 3, z11 >= 0, z = 1 + (1 + z07 + z11), z07 >= 0
   activate(z) -{ 0 }-> s54 :|: s52 >= 0, s52 <= inf12, s53 >= 0, s53 <= 2 * s52 + 3, s54 >= 0, s54 <= s53 + z1 + 1, z011 >= 0, z1 >= 0, z = 1 + (1 + z011) + z1
   activate(z) -{ 0 }-> z :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z >= 0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 0 :|: z = 0
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, z0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, z1 = v1
   activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, z - 1 = v1
   activate(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   activate(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0 + z1' :|: z - 1 >= 0, 0 = z0, z1' >= 0, z - 1 = z1', z0 >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   activate(z) -{ 0 }-> 1 + z0' + z1' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, z1 = z1', z0' >= 0
   cons(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cons(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0, v1 >= 0, 1 + (1 + z) = v1
   from(z) -{ 0 }-> 1 + z :|: z >= 0
   from(z) -{ 0 }-> 1 + z + z1 :|: z >= 0, z1 >= 0, 1 + (1 + z) = z1
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: z >= 0
   s(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {LENGTH,LENGTH1}
Previous analysis results are:
  from: runtime: O(1) [0], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [0], size: O(n^1) [1 + z]
  nil: runtime: O(1) [0], size: O(1) [0]
  ACTIVATE: runtime: O(n^1) [z], size: O(1) [0]
  activate: runtime: O(1) [0], size: EXP
  LENGTH: runtime: INF, size: O(1) [0]
  LENGTH1: runtime: ?, size: O(1) [1]

----------------------------------------

(93) 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:

   activate(v0) -> null_activate [0]
   from(v0) -> null_from [0]
   s(v0) -> null_s [0]
   nil -> null_nil [0]
   cons(v0, v1) -> null_cons [0]
   LENGTH(v0) -> null_LENGTH [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

And the following fresh constants:    null_activate, null_from, null_s, null_nil, null_cons, null_LENGTH, null_ACTIVATE, const

----------------------------------------

(94)
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:

   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) [1]
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) [1]
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) [1]
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) [1]
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) [1]
   activate(n__from(z0)) -> from(activate(z0)) [0]
   activate(n__s(z0)) -> s(activate(z0)) [0]
   activate(n__nil) -> nil [0]
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1) [0]
   activate(z0) -> z0 [0]
   from(z0) -> cons(z0, n__from(n__s(z0))) [0]
   from(z0) -> n__from(z0) [0]
   s(z0) -> n__s(z0) [0]
   nil -> n__nil [0]
   cons(z0, z1) -> n__cons(z0, z1) [0]
   activate(v0) -> null_activate [0]
   from(v0) -> null_from [0]
   s(v0) -> null_s [0]
   nil -> null_nil [0]
   cons(v0, v1) -> null_cons [0]
   LENGTH(v0) -> null_LENGTH [0]
   ACTIVATE(v0) -> null_ACTIVATE [0]

The TRS has the following type information:
LENGTH1 :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> c4
c4 :: c3:null_LENGTH -> c8:c9:c11:null_ACTIVATE -> c4
LENGTH :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> c3:null_LENGTH
activate :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
ACTIVATE :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> c8:c9:c11:null_ACTIVATE
n__cons :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
c3 :: c4 -> c8:c9:c11:null_ACTIVATE -> c3:null_LENGTH
n__from :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
c8 :: c8:c9:c11:null_ACTIVATE -> c8:c9:c11:null_ACTIVATE
n__s :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
c9 :: c8:c9:c11:null_ACTIVATE -> c8:c9:c11:null_ACTIVATE
c11 :: c8:c9:c11:null_ACTIVATE -> c8:c9:c11:null_ACTIVATE
from :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
s :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
n__nil :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
nil :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
cons :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons -> n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_activate :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_from :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_s :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_nil :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_cons :: n__cons:n__from:n__s:n__nil:null_activate:null_from:null_s:null_nil:null_cons
null_LENGTH :: c3:null_LENGTH
null_ACTIVATE :: c8:c9:c11:null_ACTIVATE
const :: c4

Rewrite Strategy: INNERMOST
----------------------------------------

(95) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   n__nil => 0
   null_activate => 0
   null_from => 0
   null_s => 0
   null_nil => 0
   null_cons => 0
   null_LENGTH => 0
   null_ACTIVATE => 0
   const => 0

----------------------------------------

(96)
Obligation:
Complexity RNTS consisting of the following rules:

   ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0
   ACTIVATE(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   LENGTH(z) -{ 1 }-> 1 + LENGTH1(activate(z1)) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   LENGTH1(z) -{ 1 }-> 1 + LENGTH(activate(z0)) + ACTIVATE(z0) :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0
   activate(z) -{ 0 }-> s(activate(z0)) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> nil :|: z = 0
   activate(z) -{ 0 }-> from(activate(z0)) :|: z = 1 + z0, z0 >= 0
   activate(z) -{ 0 }-> cons(activate(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   cons(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cons(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   from(z) -{ 0 }-> cons(z0, 1 + (1 + z0)) :|: z = z0, z0 >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   from(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   nil -{ 0 }-> 0 :|: 
   s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) by 
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))

----------------------------------------

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, ACTIVATE_1, LENGTH1_1

Compound Symbols:   c3_2, c8_1, c9_1, c11_1, c4_2


----------------------------------------

(99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, ACTIVATE_1, LENGTH1_1

Compound Symbols:   c3_2, c8_1, c9_1, c11_1, c4_2, c4_1


----------------------------------------

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) by 
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))

----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2


----------------------------------------

(103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) by 
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))

----------------------------------------

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
We considered the (Usable) Rules:none
And the Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = [1]
   POL(LENGTH1(x_1)) = [1]
   POL(activate(x_1)) = 0
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = 0
   POL(n__cons(x_1, x_2)) = x_1
   POL(n__from(x_1)) = 0
   POL(n__nil) = 0
   POL(n__s(x_1)) = 0
   POL(nil) = 0
   POL(s(x_1)) = 0

----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) by 
   LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))

----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(115) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
We considered the (Usable) Rules:none
And the Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = [2]
   POL(LENGTH1(x_1)) = [2]
   POL(activate(x_1)) = [3] + [3]x_1
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = [3]
   POL(n__cons(x_1, x_2)) = [3]
   POL(n__from(x_1)) = 0
   POL(n__nil) = [2]
   POL(n__s(x_1)) = [1]
   POL(nil) = 0
   POL(s(x_1)) = 0

----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) by 
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))

----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1


----------------------------------------

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__nil) -> c4(LENGTH(nil)) by 
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))

----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1


----------------------------------------

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))

----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1


----------------------------------------

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) by 
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))

----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1


----------------------------------------

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) by 
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))

----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1


----------------------------------------

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) by 
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))

----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1


----------------------------------------

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) by 
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))

----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1


----------------------------------------

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) by 
   LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0)))

----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1


----------------------------------------

(133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1


----------------------------------------

(135) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0)))

----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1


----------------------------------------

(137) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) by LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil)))
----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil)))
S tuples:
   ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0))
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1


----------------------------------------

(139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) by 
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))

----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
S tuples:
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c9_1, c11_1, c4_2, c3_2, c4_1, c3_1, c8_1


----------------------------------------

(141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
S tuples:
   ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0))
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c9_1, c11_1, c4_2, c3_2, c4_1, c3_1, c8_1


----------------------------------------

(143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) by 
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))

----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
S tuples:
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil)))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c11_1, c4_2, c3_2, c4_1, c3_1, c8_1, c9_1


----------------------------------------

(145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
S tuples:
   ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0))
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   ACTIVATE_1, LENGTH1_1, LENGTH_1

Compound Symbols:   c11_1, c4_2, c3_2, c4_1, c3_1, c8_1, c9_1


----------------------------------------

(147) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) by 
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))

----------------------------------------

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1


----------------------------------------

(149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1


----------------------------------------

(151) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) by LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1


----------------------------------------

(153) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) by 
   LENGTH1(n__cons(y0, y1)) -> c4(LENGTH(n__cons(y0, y1)), ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))

----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c3_1, c8_1, c9_1, c11_1


----------------------------------------

(155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))

----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing tuple parts
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(159) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
We considered the (Usable) Rules:none
And the Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = [1]
   POL(LENGTH1(x_1)) = [1]
   POL(activate(x_1)) = 0
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = 0
   POL(n__cons(x_1, x_2)) = 0
   POL(n__from(x_1)) = 0
   POL(n__nil) = 0
   POL(n__s(x_1)) = 0
   POL(nil) = 0
   POL(s(x_1)) = 0

----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(161) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
We considered the (Usable) Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   cons(z0, z1) -> n__cons(z0, z1)
And the Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = x_1
   POL(LENGTH1(x_1)) = [1]
   POL(activate(x_1)) = 0
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1]
   POL(from(x_1)) = [1]
   POL(n__cons(x_1, x_2)) = [1]
   POL(n__from(x_1)) = 0
   POL(n__nil) = 0
   POL(n__s(x_1)) = 0
   POL(nil) = 0
   POL(s(x_1)) = 0

----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(163) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) by LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
----------------------------------------

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(165) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) by LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1


----------------------------------------

(167) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) by LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c3_1, c11_1


----------------------------------------

(169) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil))) by LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)))
----------------------------------------

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c3_1, c11_1


----------------------------------------

(171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)))

----------------------------------------

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c3_1, c11_1


----------------------------------------

(173) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) by LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil)))
----------------------------------------

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil))) by 
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))

----------------------------------------

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(177) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) by LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0)))
----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(179) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) by LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1)))
----------------------------------------

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(181) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) by LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
----------------------------------------

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(183) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) by LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0))
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1, ACTIVATE_1

Compound Symbols:   c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(185) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) by 
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(y0))) -> c3(LENGTH1(n__s(y0)), ACTIVATE(n__s(y0)))
   LENGTH(n__cons(z0, n__cons(y0, y1))) -> c3(LENGTH1(n__cons(y0, y1)), ACTIVATE(n__cons(y0, y1)))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0)))

----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(189) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
We considered the (Usable) Rules:none
And the Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = [1]
   POL(LENGTH1(x_1)) = [1]
   POL(activate(x_1)) = 0
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(from(x_1)) = 0
   POL(n__cons(x_1, x_2)) = 0
   POL(n__from(x_1)) = 0
   POL(n__nil) = 0
   POL(n__s(x_1)) = 0
   POL(nil) = [1]
   POL(s(x_1)) = 0

----------------------------------------

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(191) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
We considered the (Usable) Rules:
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   cons(z0, z1) -> n__cons(z0, z1)
And the Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ACTIVATE(x_1)) = 0
   POL(LENGTH(x_1)) = x_1
   POL(LENGTH1(x_1)) = x_1
   POL(activate(x_1)) = 0
   POL(c11(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1)) = x_1
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1]
   POL(from(x_1)) = [1]
   POL(n__cons(x_1, x_2)) = [1]
   POL(n__from(x_1)) = [1]
   POL(n__nil) = 0
   POL(n__s(x_1)) = 0
   POL(nil) = [1]
   POL(s(x_1)) = 0

----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0)))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(193) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) by 
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))

----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(195) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) by 
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))

----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1


----------------------------------------

(197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0))) by 
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))

----------------------------------------

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1


----------------------------------------

(199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil)))

----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1


----------------------------------------

(201) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) by 
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))

----------------------------------------

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1


----------------------------------------

(203) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) by 
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))

----------------------------------------

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1


----------------------------------------

(205) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) by 
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))

----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1


----------------------------------------

(207) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) by 
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))

----------------------------------------

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1


----------------------------------------

(209) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) by 
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))

----------------------------------------

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1


----------------------------------------

(211) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) by 
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))

----------------------------------------

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1


----------------------------------------

(213) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) by 
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))

----------------------------------------

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
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   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1


----------------------------------------

(215) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) by 
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))

----------------------------------------

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(217) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) by 
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))

----------------------------------------

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
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   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(219) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) by 
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))

----------------------------------------

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(221) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) by 
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))

----------------------------------------

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(223) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) by 
   ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))

----------------------------------------

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
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   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(225) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) by 
   ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))))

----------------------------------------

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(activate(z0))
   activate(n__s(z0)) -> s(activate(z0))
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(activate(z0), z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(n__s(z0)))
   from(z0) -> n__from(z0)
   s(z0) -> n__s(z0)
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
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   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))))
S tuples:
   LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0)))
   LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1)))
   LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1)))
   LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1)))
   LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1)))
   LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0))))
   LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0))))
   LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1)))
   LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2)))
   LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2)))
   LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)))
   ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2)))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil)))
   LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0)))
   LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0)))
   LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0))))
   LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0))))
   LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1)))
   LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2)))
   LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1)))
   LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1)))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2)))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1))))
   LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)))
   ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0))))
   ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0))))
   ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0))))
   ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1))))
   ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)))
   ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))
   ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))))
   ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))))
   ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))))
   ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0)))))
   ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1)))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0))))))
   ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))))
K tuples:
   LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0))))
   LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0))))
   LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1))))
   LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0))))
   LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
   LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil)))
   LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1)))
   LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0))))
   LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0))))
   LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1))))
   LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1)))
   LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0))))
   LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0))))
   LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1))))
   LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0)))))
   LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1)))))
Defined Rule Symbols:   activate_1, from_1, s_1, nil, cons_2

Defined Pair Symbols:   LENGTH1_1, LENGTH_1, ACTIVATE_1

Compound Symbols:   c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1


----------------------------------------

(227) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(228)
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:

   from(X) -> cons(X, n__from(n__s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   s(X) -> n__s(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(activate(X)) [1]
   activate(n__s(X)) -> s(activate(X)) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1]
   activate(X) -> X [1]

Rewrite Strategy: INNERMOST
----------------------------------------

(229) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(230)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   from(X) -> cons(X, n__from(n__s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   s(X) -> n__s(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(activate(X)) [1]
   activate(n__s(X)) -> s(activate(X)) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1]
   activate(X) -> X [1]

The TRS has the following type information:
from :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
cons :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
n__from :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
n__s :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
length :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
n__nil :: n__s:n__from:n__nil:0:n__cons
0 :: n__s:n__from:n__nil:0:n__cons
n__cons :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
s :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
length1 :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
activate :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons
nil :: n__s:n__from:n__nil:0:n__cons

Rewrite Strategy: INNERMOST
----------------------------------------

(231) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   activate_1
   length1_1
   length_1
   s_1
   from_1
   cons_2
   nil

Due to the following rules being added:

   length(v0) -> null_length [0]

And the following fresh constants:    null_length

----------------------------------------

(232)
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:

   from(X) -> cons(X, n__from(n__s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   s(X) -> n__s(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(activate(X)) [1]
   activate(n__s(X)) -> s(activate(X)) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1]
   activate(X) -> X [1]
   length(v0) -> null_length [0]

The TRS has the following type information:
from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__nil :: n__s:n__from:n__nil:0:n__cons:null_length
0 :: n__s:n__from:n__nil:0:n__cons:null_length
n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
nil :: n__s:n__from:n__nil:0:n__cons:null_length
null_length :: n__s:n__from:n__nil:0:n__cons:null_length

Rewrite Strategy: INNERMOST
----------------------------------------

(233) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(234)
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:

   from(X) -> cons(X, n__from(n__s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, n__from(X'))) -> s(length1(from(activate(X')))) [2]
   length(n__cons(X, n__s(X''))) -> s(length1(s(activate(X'')))) [2]
   length(n__cons(X, n__nil)) -> s(length1(nil)) [2]
   length(n__cons(X, n__cons(X1', X2'))) -> s(length1(cons(activate(X1'), X2'))) [2]
   length(n__cons(X, Y)) -> s(length1(Y)) [2]
   length1(n__from(X3)) -> length(from(activate(X3))) [2]
   length1(n__s(X4)) -> length(s(activate(X4))) [2]
   length1(n__nil) -> length(nil) [2]
   length1(n__cons(X1'', X2'')) -> length(cons(activate(X1''), X2'')) [2]
   length1(X) -> length(X) [2]
   from(X) -> n__from(X) [1]
   s(X) -> n__s(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(n__from(X5))) -> from(from(activate(X5))) [2]
   activate(n__from(n__s(X6))) -> from(s(activate(X6))) [2]
   activate(n__from(n__nil)) -> from(nil) [2]
   activate(n__from(n__cons(X11, X21))) -> from(cons(activate(X11), X21)) [2]
   activate(n__from(X)) -> from(X) [2]
   activate(n__s(n__from(X7))) -> s(from(activate(X7))) [2]
   activate(n__s(n__s(X8))) -> s(s(activate(X8))) [2]
   activate(n__s(n__nil)) -> s(nil) [2]
   activate(n__s(n__cons(X12, X22))) -> s(cons(activate(X12), X22)) [2]
   activate(n__s(X)) -> s(X) [2]
   activate(n__nil) -> nil [1]
   activate(n__cons(n__from(X9), X2)) -> cons(from(activate(X9)), X2) [2]
   activate(n__cons(n__s(X10), X2)) -> cons(s(activate(X10)), X2) [2]
   activate(n__cons(n__nil, X2)) -> cons(nil, X2) [2]
   activate(n__cons(n__cons(X13, X23), X2)) -> cons(cons(activate(X13), X23), X2) [2]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [2]
   activate(X) -> X [1]
   length(v0) -> null_length [0]

The TRS has the following type information:
from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__nil :: n__s:n__from:n__nil:0:n__cons:null_length
0 :: n__s:n__from:n__nil:0:n__cons:null_length
n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
nil :: n__s:n__from:n__nil:0:n__cons:null_length
null_length :: n__s:n__from:n__nil:0:n__cons:null_length

Rewrite Strategy: INNERMOST
----------------------------------------

(235) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   n__nil => 1
   0 => 0
   null_length => 0

----------------------------------------

(236)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 2 }-> s(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 2 }-> s(s(activate(X8))) :|: X8 >= 0, z = 1 + (1 + X8)
   activate(z) -{ 2 }-> s(nil) :|: z = 1 + 1
   activate(z) -{ 2 }-> s(from(activate(X7))) :|: X7 >= 0, z = 1 + (1 + X7)
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 1 }-> nil :|: z = 1
   activate(z) -{ 2 }-> from(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 2 }-> from(s(activate(X6))) :|: X6 >= 0, z = 1 + (1 + X6)
   activate(z) -{ 2 }-> from(nil) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(from(activate(X5))) :|: X5 >= 0, z = 1 + (1 + X5)
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(nil, X2) :|: z = 1 + 1 + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(nil)) :|: z = 1 + X + 1, X >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X
   length1(z) -{ 2 }-> length(s(activate(X4))) :|: z = 1 + X4, X4 >= 0
   length1(z) -{ 2 }-> length(nil) :|: z = 1
   length1(z) -{ 2 }-> length(from(activate(X3))) :|: z = 1 + X3, X3 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X


----------------------------------------

(237) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   nil -{ 1 }-> 1 :|: 
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

----------------------------------------

(238)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 2 }-> s(s(activate(X8))) :|: X8 >= 0, z = 1 + (1 + X8)
   activate(z) -{ 2 }-> s(from(activate(X7))) :|: X7 >= 0, z = 1 + (1 + X7)
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(X6))) :|: X6 >= 0, z = 1 + (1 + X6)
   activate(z) -{ 2 }-> from(from(activate(X5))) :|: X5 >= 0, z = 1 + (1 + X5)
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z = 1 + 1 + X2, X2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, X2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 2 }-> 1 + X1 + X2 :|: X >= 0, z = X, X1 >= 0, X2 >= 0, X = X1, 1 + (1 + X) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z = 1 + X + 1, X >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X
   length1(z) -{ 2 }-> length(s(activate(X4))) :|: z = 1 + X4, X4 >= 0
   length1(z) -{ 2 }-> length(from(activate(X3))) :|: z = 1 + X3, X3 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X


----------------------------------------

(239) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(240)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0


----------------------------------------

(241) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { nil }
   { from }
   { cons }
   { s }
   { activate }
   { length1, length }

----------------------------------------

(242)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length}

----------------------------------------

(243) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(244)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length}

----------------------------------------

(245) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(246)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: ?, size: O(1) [1]

----------------------------------------

(247) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(248)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(249) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(250)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(251) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

----------------------------------------

(252)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: ?, size: O(n^1) [3 + 2*z]

----------------------------------------

(253) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(254)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]

----------------------------------------

(255) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(256)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]

----------------------------------------

(257) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

----------------------------------------

(258)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: ?, size: O(n^1) [1 + z + z']

----------------------------------------

(259) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(260)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']

----------------------------------------

(261) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(262)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']

----------------------------------------

(263) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: s
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(264)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {s}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(265) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: s
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(266)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 3 }-> s(1) :|: z = 1 + 1
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]

----------------------------------------

(267) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(268)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]

----------------------------------------

(269) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

----------------------------------------

(270)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]
  activate: runtime: ?, size: EXP

----------------------------------------

(271) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 30 + 37*z

----------------------------------------

(272)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0
   activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0
   length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]
  activate: runtime: O(n^1) [30 + 37*z], size: EXP

----------------------------------------

(273) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(274)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0
   activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0
   length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0
   length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]
  activate: runtime: O(n^1) [30 + 37*z], size: EXP

----------------------------------------

(275) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: length1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: length
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

----------------------------------------

(276)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0
   activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0
   length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0
   length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]
  activate: runtime: O(n^1) [30 + 37*z], size: EXP
  length1: runtime: ?, size: INF
  length: runtime: ?, size: INF

----------------------------------------

(277) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: length1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

----------------------------------------

(278)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1
   activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0
   activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0
   activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0
   activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0
   activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0
   activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0
   activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 1 :|: z = 1
   activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2'
   activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0
   length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: z >= 0
   length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0
   length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0
   length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(1) :|: z = 1
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [1]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  s: runtime: O(1) [1], size: O(n^1) [1 + z]
  activate: runtime: O(n^1) [30 + 37*z], size: EXP
  length1: runtime: INF, size: INF
  length: runtime: ?, size: INF

----------------------------------------

(279) 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:

   length(v0) -> null_length [0]

And the following fresh constants:    null_length

----------------------------------------

(280)
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:

   from(X) -> cons(X, n__from(n__s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   s(X) -> n__s(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(activate(X)) [1]
   activate(n__s(X)) -> s(activate(X)) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1]
   activate(X) -> X [1]
   length(v0) -> null_length [0]

The TRS has the following type information:
from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
n__nil :: n__s:n__from:n__nil:0:n__cons:null_length
0 :: n__s:n__from:n__nil:0:n__cons:null_length
n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length
nil :: n__s:n__from:n__nil:0:n__cons:null_length
null_length :: n__s:n__from:n__nil:0:n__cons:null_length

Rewrite Strategy: INNERMOST
----------------------------------------

(281) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   n__nil => 1
   0 => 0
   null_length => 0

----------------------------------------

(282)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> s(activate(X)) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> nil :|: z = 1
   activate(z) -{ 1 }-> from(activate(X)) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> cons(activate(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   length(z) -{ 1 }-> s(length1(activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 1 }-> 0 :|: z = 1
   length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length1(z) -{ 1 }-> length(activate(X)) :|: X >= 0, z = X
   nil -{ 1 }-> 1 :|: 
   s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

Only complete derivations are relevant for the runtime complexity.